void tdo_scheme::exit_partition_stack()
{
if (the_row_scheme) {
FREE_int(the_row_scheme);
the_row_scheme = NULL;
}
if (the_col_scheme) {
FREE_int(the_col_scheme);
the_col_scheme = NULL;
}
if (the_extra_row_scheme) {
FREE_int(the_extra_row_scheme);
the_extra_row_scheme = NULL;
}
if (the_extra_col_scheme) {
FREE_int(the_extra_col_scheme);
the_extra_col_scheme = NULL;
}
free_partition(ROW);
free_partition(COL);
//if (extra_row_level >= 0)
free_partition(EXTRA_ROW);
//if (extra_col_level >= 0)
free_partition(EXTRA_COL);
free_partition(LAMBDA);
}
void blt_set_invariants::freeself()
{
if (the_set_in_orthogonal) {
FREE_int(the_set_in_orthogonal);
}
if (the_set_in_PG) {
FREE_int(the_set_in_PG);
}
}
vector_hashing::~vector_hashing()
{
if (vector_data) {
FREE_int(vector_data);
vector_data = NULL;
}
if (H) {
FREE_int(H);
H = NULL;
}
if (H_sorted) {
FREE_int(H_sorted);
H_sorted = NULL;
}
if (perm) {
FREE_int(perm);
perm = NULL;
}
if (perm_inv) {
FREE_int(perm_inv);
perm_inv = NULL;
}
if (type_first) {
FREE_int(type_first);
type_first = NULL;
}
if (type_len) {
FREE_int(type_len);
type_len = NULL;
}
if (type_value) {
FREE_int(type_value);
type_value = NULL;
}
}
void partial_derivative::freeself()
{
if (mapping) {
FREE_int(mapping);
}
null();
}
void flag_orbit_node::freeself()
{
if (fusion_elt) {
FREE_int(fusion_elt);
}
if (gens) {
FREE_OBJECT(gens);
}
null();
}
void tdo_scheme::init_part_and_entries(int *Part, int *Entries, INT verbose_level)
{
int i;
INT f_v = (verbose_level >= 1);
for (part_length = 0; ; part_length++) {
if (Part[part_length] == -1)
break;
}
if (f_v) {
cout << "partition of length " << part_length << endl;
}
for (nb_entries = 0; ; nb_entries++) {
if (Entries[4 * nb_entries + 0] == -1)
break;
}
if (f_v) {
cout << "nb_entries = " << nb_entries << endl;
}
if (part) {
FREE_int(part);
}
if (entries) {
FREE_int(entries);
}
part = NEW_int(part_length + 1);
for (i = 0; i <= part_length; i++) {
part[i] = Part[i];
}
entries = NEW_int(4 * nb_entries + 1);
for (i = 0; i <= 4 * nb_entries; i++) {
entries[i] = Entries[i];
}
}
tdo_scheme::~tdo_scheme()
{
INT i;
if (part) {
FREE_int(part);
part = NULL;
}
if (entries) {
FREE_int(entries);
entries = NULL;
}
for (i = 0; i < NUMBER_OF_SCHEMES; i++) {
free_partition(i);
}
if (the_row_scheme) {
FREE_int(the_row_scheme);
the_row_scheme = NULL;
}
if (the_col_scheme) {
FREE_int(the_col_scheme);
the_col_scheme = NULL;
}
if (the_extra_row_scheme) {
FREE_int(the_extra_row_scheme);
the_extra_row_scheme = NULL;
}
if (the_extra_col_scheme) {
FREE_int(the_extra_col_scheme);
the_extra_col_scheme = NULL;
}
if (the_row_scheme_cur) {
FREE_INT(the_row_scheme_cur);
the_row_scheme_cur = NULL;
}
if (the_col_scheme_cur) {
FREE_INT(the_col_scheme_cur);
the_col_scheme_cur = NULL;
}
if (the_extra_row_scheme_cur) {
FREE_INT(the_extra_row_scheme_cur);
the_extra_row_scheme_cur = NULL;
}
if (the_extra_col_scheme_cur) {
FREE_INT(the_extra_col_scheme_cur);
the_extra_col_scheme_cur = NULL;
}
if (P) {
delete P;
P = NULL;
}
}
void blt_set_invariants::latex(ostream &ost, int verbose_level)
{
int f_v = (verbose_level >= 1);
sorting Sorting;
if (f_v) {
cout << "blt_set_invariants::latex" << endl;
}
int a, i, j;
ost << "Plane intersection type is ";
for (i = highest_intersection_number; i >= 0; i--) {
a = intersection_type[i];
if (a == 0)
continue;
ost << "$" << i;
if (a > 9) {
ost << "^{" << a << "}";
}
else if (a > 1) {
ost << "^" << a;
}
ost << "$ ";
}
ost << "\\\\" << endl;
ost << "Plane invariant is ";
if (nb_planes < 10) {
ost << "$$";
ost << "\\left[" << endl;
ost << "\\begin{array}{*{" << nb_planes << "}{c}}" << endl;
for (i = 0; i < nb_planes; i++) {
for (j = 0; j < nb_planes; j++) {
ost << intersection_matrix[i * nb_planes + j];
if (j < nb_planes - 1) {
ost << " & ";
}
}
ost << "\\\\" << endl;
}
ost << "\\end{array}" << endl;
ost << "\\right]" << endl;
ost << "$$" << endl;
}
else {
ost << "too big (" << nb_planes << " planes)\\\\" << endl;
}
int f_enter_math = FALSE;
int f_print_subscripts = TRUE;
ost << "$$" << endl;
D2->print_row_decomposition_tex(
ost, f_enter_math, f_print_subscripts, verbose_level - 1);
ost << "\\quad" << endl;
D2->print_column_decomposition_tex(
ost, f_enter_math, f_print_subscripts, verbose_level - 1);
ost << "$$" << endl;
D2->Stack->print_classes_tex(ost);
if (Sos3->nb_sets) {
ost << "$$" << endl;
D3->print_row_decomposition_tex(
ost, f_enter_math, f_print_subscripts, verbose_level - 1);
ost << "$$" << endl;
ost << "$$" << endl;
D3->print_column_decomposition_tex(
ost, f_enter_math, f_print_subscripts, verbose_level - 1);
ost << "$$" << endl;
D3->Stack->print_classes_tex(ost);
int t, fst_col, fst, len, u, a;
fst_col = D3->Stack->startCell[1];
for (t = 0; t < D3->Stack->ht; t++) {
if (!D3->Stack->is_col_class(t)) {
continue;
}
ost << "Column cell " << t << ":\\\\" << endl;
len = D3->Stack->cellSize[t];
fst = D3->Stack->startCell[t];
int *Cell;
Cell = NEW_int(len);
for (u = 0; u < len; u++) {
a = D3->Stack->pointList[fst + u] - fst_col;
Cell[u] = a;
}
Sorting.int_vec_heapsort(Cell, len);
#if 0
for (u = 0; u < len; u++) {
a = Cell[u];
b = Sos3_idx[h][a];
f << a << " (rank = ";
R[h][b].print_not_scientific(f);
f << ") = ";
G->unrank_longinteger(R[h][b], 0 /* verbose_level */);
f << "$\\left[" << endl;
f << "\\begin{array}{*{" << 5 << "}{c}}" << endl;
for (i = 0; i < 3; i++) {
for (j = 0; j < 5; j++) {
c = G->M[i * 5 + j];
f << c;
if (j < 4) {
f << "&";
}
}
f << "\\\\" << endl;
}
f << "\\end{array}" << endl;
f << "\\right]$\\\\" << endl;
}
#endif
FREE_int(Cell);
}
}
int tt, u, v;
tt = (set_size + 3) / 4;
ost << "The points by ranks:\\\\" << endl;
ost << "\\begin{center}" << endl;
for (u = 0; u < 4; u++) {
ost << "\\begin{tabular}[t]{|c|c|}" << endl;
ost << "\\hline" << endl;
ost << "$i$ & Rank \\\\" << endl;
ost << "\\hline" << endl;
for (i = 0; i < tt; i++) {
v = u * tt + i;
if (v < set_size) {
ost << "$" << v << "$ & $" << the_set_in_orthogonal[v]
<< "$ \\\\" << endl;
}
}
ost << "\\hline" << endl;
ost << "\\end{tabular}" << endl;
}
ost << "\\end{center}" << endl;
ost << "The points:\\\\" << endl;
int v5[5];
for (i = 0; i < set_size; i++) {
D->O->unrank_point(
v5, 1, the_set_in_orthogonal[i], 0 /* verbose_level */);
//Grass->unrank_int(data[i], 0/*verbose_level - 4*/);
if ((i % 4) == 0) {
if (i) {
ost << "$$" << endl;
}
ost << "$$" << endl;
}
//f << "\\left[" << endl;
//f << "\\begin{array}{c}" << endl;
ost << "P_{" << i /*data[i]*/ << "}=";
int_vec_print(ost, v5, 5);
#if 0
for (u = 0; u < 5; u++) {
for (v = 0; v < n; v++) {
f << Grass->M[u * n + v];
}
ost << "\\\\" << endl;
}
#endif
//f << "\\end{array}" << endl;
//f << "\\right]" << endl;
}
ost << "$$" << endl;
if (f_v) {
cout << "blt_set_invariants::latex done" << endl;
}
}
void tdo_scheme::init_partition_stack(int verbose_level)
{
int k, at, f, c, l, i;
int f_v = (verbose_level >= 1);
int f_vv = (verbose_level >= 2);
int f_vvv = (verbose_level >= 3);
if (f_v) {
cout << "tdo_scheme::init_partition_stack" << endl;
}
if (f_vv) {
cout << "part_length=" << part_length << endl;
cout << "row_level=" << row_level << endl;
cout << "col_level=" << col_level << endl;
cout << "verbose_level=" << verbose_level << endl;
}
mn = part[0];
m = part[1];
n = mn - m;
if (part_length < 2) {
cout << "part_length < 2" << endl;
exit(1);
}
if (f_vvv) {
cout << "init_partition_stack: m=" << m << " n=" << n << endl;
int_vec_print(part, part_length + 1);
cout << endl;
}
P = new partitionstack;
P->allocate(m + n, 0 /* verbose_level */);
//PB.init_partition_backtrack_basic(m, n, verbose_level - 10);
if (f_vvv) {
cout << "after PB.init_partition_backtrack_basic" << endl;
}
//partitionstack &P = PB.P;
if (f_vvv) {
cout << "initial partition stack: " << endl;
P->print(cout);
}
for (k = 1; k < part_length; k++) {
at = part[k];
c = P->cellNumber[at];
f = P->startCell[c];
l = P->cellSize[c];
if (f_vvv) {
cout << "part[" << k << "]=" << at << endl;
cout << "P->cellNumber[at]=" << c << endl;
cout << "P->startCell[c]=" << f << endl;
cout << "P->cellSize[c]=" << l << endl;
cout << "f + l - at=" << f + l - at << endl;
}
P->subset_continguous(at, f + l - at);
P->split_cell(FALSE);
if (f_vvv) {
cout << "after splitting at " << at << endl;
P->print(cout);
}
if (P->ht == row_level) {
l = P->ht;
if (the_row_scheme) {
FREE_int(the_row_scheme);
the_row_scheme = NULL;
}
the_row_scheme = NEW_int(l * l);
for (i = 0; i < l * l; i++) {
the_row_scheme[i] = -1;
}
get_partition(ROW, l, verbose_level - 3);
get_row_or_col_scheme(ROW, l, verbose_level - 3);
}
if (P->ht == col_level) {
l = P->ht;
if (the_col_scheme) {
FREE_int(the_col_scheme);
the_col_scheme = NULL;
}
the_col_scheme = NEW_int(l * l);
for (i = 0; i < l * l; i++) {
the_col_scheme[i] = -1;
}
get_partition(COL, l, verbose_level - 3);
get_row_or_col_scheme(COL, l, verbose_level - 3);
}
if (P->ht == extra_row_level) {
l = P->ht;
if (the_extra_row_scheme) {
FREE_int(the_extra_row_scheme);
the_extra_row_scheme = NULL;
}
the_extra_row_scheme = NEW_int(l * l);
for (i = 0; i < l * l; i++) {
the_extra_row_scheme[i] = -1;
}
get_partition(EXTRA_ROW, l, verbose_level - 3);
get_row_or_col_scheme(EXTRA_ROW, l, verbose_level - 3);
}
if (P->ht == extra_col_level) {
l = P->ht;
if (the_extra_col_scheme) {
FREE_int(the_extra_col_scheme);
the_extra_col_scheme = NULL;
}
the_extra_col_scheme = NEW_int(l * l);
for (i = 0; i < l * l; i++) {
the_extra_col_scheme[i] = -1;
}
get_partition(EXTRA_COL, l, verbose_level - 3);
get_row_or_col_scheme(EXTRA_COL, l, verbose_level - 3);
}
if (P->ht == lambda_level) {
l = P->ht;
get_partition(LAMBDA, l, verbose_level - 3);
}
} // next k
if (f_vvv) {
cout << "before complete_partition_info" << endl;
}
if (row_level >= 2) {
complete_partition_info(ROW, 0/*verbose_level*/);
}
if (col_level >= 2) {
complete_partition_info(COL, 0/*verbose_level*/);
}
if (extra_row_level >= 2) {
complete_partition_info(EXTRA_ROW, 0/*verbose_level*/);
}
if (extra_col_level >= 2 && extra_col_level < part_length) {
complete_partition_info(EXTRA_COL, 0/*verbose_level*/);
}
complete_partition_info(LAMBDA, 0/*verbose_level*/);
if (f_vv) {
if (row_level >= 2) {
print_scheme(ROW, FALSE);
}
if (col_level >= 2) {
print_scheme(COL, FALSE);
}
if (extra_row_level >= 2) {
print_scheme(EXTRA_ROW, FALSE);
}
if (extra_col_level >= 2) {
print_scheme(EXTRA_COL, FALSE);
}
print_scheme(LAMBDA, FALSE);
}
}
void coding_theory_domain::make_tensor_code_9_dimensional(int q,
const char *override_poly_Q, const char *override_poly,
int f_hyperoval,
int *&code, int &length,
int verbose_level)
{
finite_field F;
finite_field f;
rank_checker rc;
int exponents[9];
int *M;
int *C;
int *C_inv;
int *H;
int *H_subfield;
int index, Q, i, j, t, m, n, r, beta, beta_q;
int f_v = (verbose_level >= 1);
int f_vv = (verbose_level >= 2);
if (f_v) {
cout << "make_tensor_code_9_dimensional q=" << q << endl;
}
//q = 2; override_poly_Q = ""; override_poly = ""; int f_hyperoval = FALSE;
//q = 3; override_poly_Q = ""; override_poly = ""; int f_hyperoval = FALSE;
//q = 4; override_poly_Q = "19"; override_poly = "7"; int f_hyperoval = FALSE;
// F_256 generated by X^8 + X^4 + X^3 + X^2 + 1
// F_16 generated by X^4+X+1 = 19
// F_4 generated by X^2+X+1 = 7
//q = 5; override_poly_Q = "47"; override_poly = ""; int f_hyperoval = FALSE;
// F_625 generated by X^4 + X^3 + 3X + 2
// F_25 generated by X^2 + 4X + 2 = 47
//q = 7; override_poly_Q = ""; override_poly = ""; int f_hyperoval = FALSE;
//q = 8; override_poly_Q = "97"; override_poly = "11"; int f_hyperoval = TRUE;
// F_4096 generated by x^12+x^6+x^4+x+1
// F_64 generated by X^6+X^5+1 = 97
// F_8 generated by X^3+X+1 = 11
//q = 9; override_poly_Q = ""; override_poly = "17"; int f_hyperoval = FALSE;
beta = q;
Q = q * q;
m = 9;
if (f_hyperoval) {
n = Q + 2;
}
else {
n = Q + 1;
}
r = 5;
if (q == 4)
r = 7;
if (q == 3)
r = 9;
exponents[0] = 0;
exponents[1] = q + 1;
exponents[2] = 2 * q + 2;
exponents[3] = q;
exponents[4] = 1;
exponents[5] = 2 * q;
exponents[6] = 2;
exponents[7] = 2 * q + 1;
exponents[8] = q + 2;
//exponents[0] = 0;
//exponents[1] = q;
//exponents[2] = 2 * q;
//exponents[3] = 1;
//exponents[4] = q + 1;
//exponents[5] = 2 * q + 1;
//exponents[6] = 2;
//exponents[7] = q + 2;
//exponents[8] = 2 * q + 2;
index = (Q - 1) / (q - 1);
cout << "q = " << q << " override polynomial = " << override_poly << endl;
cout << "Q = " << Q << endl;
F.init_override_polynomial(Q, override_poly_Q, verbose_level);
cout << "field of order " << Q << " initialized" << endl;
beta_q = F.power(beta, q);
f.init_override_polynomial(q, override_poly, verbose_level);
cout << "field of order " << q << " initialized" << endl;
cout << "n = " << n << endl;
cout << "index = " << index << endl;
cout << "beta = " << beta << endl;
cout << "beta_q = " << beta_q << endl;
F.compute_subfields(verbose_level - 3);
M = NEW_int(m * n);
C = NEW_int(m * m);
C_inv = NEW_int(m * m);
H = NEW_int(m * n);
H_subfield = NEW_int(m * n);
rc.init(&f, m, n, r + 1);
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
M[i * n + j] = 0;
}
}
for (i = 0; i < m; i++) {
for (j = 0; j < m; j++) {
C[i * m + j] = 0;
}
}
for (t = 0; t < Q; t++) {
for (i = 0; i < m; i++) {
M[i * n + t] = F.power(t, exponents[i]);
}
}
{
M[2 * n + Q] = 1;
if (f_hyperoval)
M[1 * n + Q + 1] = 1;
int nb_C_coeffs = 15;
int k, aa;
int C_coeffs[] = {
0, 0, 1,
1, 1, 1,
2, 2, 1,
3, 3, 1,
3, 4, 1,
4, 3, beta_q,
4, 4, beta,
5, 5, 1,
5, 6, 1,
6, 5, beta_q,
6, 6, beta,
7, 7, 1,
7, 8, 1,
8, 7, beta_q,
8, 8, beta,
};
for (k = 0; k < nb_C_coeffs; k++) {
i = C_coeffs[k * 3 + 0];
j = C_coeffs[k * 3 + 1];
aa = C_coeffs[k * 3 + 2];
C[i * m + j] = aa;
}
}
cout << "M:" << endl;
print_integer_matrix_width(cout, M, m, n, n, 2);
{
int *all_one, *col_sum;
all_one = NEW_int(n);
col_sum = NEW_int(m);
for (i = 0; i < n; i++)
all_one[i] = 1;
F.mult_matrix_matrix(M, all_one, col_sum, m, n, 1,
0 /* verbose_level */);
cout << "col_sum:" << endl;
print_integer_matrix_width(cout, col_sum, m, 1, 1, 2);
FREE_int(all_one);
FREE_int(col_sum);
}
#if 0
for (j = 0; j < n; j++) {
PG_element_normalize(F, M + j, n, m);
}
cout << "column normalized M:" << endl;
print_integer_matrix_width(cout, M, m, n, n, 2);
#endif
cout << "C:" << endl;
print_integer_matrix_width(cout, C, m, m, m, 2);
F.invert_matrix(C, C_inv, m);
cout << "C_inv:" << endl;
print_integer_matrix_width(cout, C_inv, m, m, m, 2);
{
int *AA;
AA = NEW_int(m * m);
F.mult_matrix_matrix(C, C_inv, AA, m, m, m,
0 /* verbose_level */);
cout << "C * C_inv:" << endl;
print_integer_matrix_width(cout, AA, m, m, m, 2);
FREE_int(AA);
}
F.mult_matrix_matrix(C, M, H, m, m, n,
0 /* verbose_level */);
cout << "H = C * M:" << endl;
print_integer_matrix_width(cout, H, m, n, n, 2);
#if 0
rk = F.Gauss_int(M, FALSE /* f_special */, TRUE /* f_complete */, base_cols,
FALSE /* f_P */, NULL, m /* m */, n /* n */, 0 /* Pn */,
FALSE, FALSE);
cout << "has rank " << rk << endl;
#endif
if (f_vv) {
cout << "before field reduction:" << endl;
print_integer_matrix_width(cout, H, m, n, n, 2);
cout << endl;
f.print_integer_matrix_zech(cout, H, m, n);
cout << endl;
}
F.retract_int_vec(f, 2, H, H_subfield, m * n, 0 /* verbose_level */);
//field_reduction(F, f, m, n, H, H_subfield, TRUE, TRUE);
if (f_vv) {
cout << "after field reduction:" << endl;
print_integer_matrix_width(cout, H_subfield, m, n, n, 2);
cout << endl;
f.print_integer_matrix_zech(cout, H_subfield, m, n);
cout << endl;
}
cout << "H_subfield:" << endl;
print_integer_matrix_width(cout, H_subfield, m, n, n, 2);
code = H_subfield;
length = n;
FREE_int(M);
FREE_int(C);
FREE_int(C_inv);
FREE_int(H);
}
void coding_theory_domain::make_tensor_code_9dimensional_as_point_set(
finite_field *F,
int *&the_set, int &length,
int verbose_level)
{
int f_v = (verbose_level >= 1);
int f_hyperoval = FALSE;
const char *override_poly = "";
const char *override_poly_Q = "";
int i, t, q;
int *code;
if (f_v) {
cout << "make_tensor_code_9dimensional_as_point_set" << endl;
}
q = F->q;
if (q == 2) {
override_poly_Q = ""; override_poly = ""; f_hyperoval = FALSE;
}
else if (q == 3) {
override_poly_Q = ""; override_poly = ""; f_hyperoval = FALSE;
}
else if (q == 4) {
override_poly_Q = "19"; override_poly = "7"; f_hyperoval = FALSE;
// F_256 generated by X^8 + X^4 + X^3 + X^2 + 1
// F_16 generated by X^4+X+1 = 19
// F_4 generated by X^2+X+1 = 7
}
else if (q == 5) {
override_poly_Q = "47"; override_poly = ""; f_hyperoval = FALSE;
// F_625 generated by X^4 + X^3 + 3X + 2
// F_25 generated by X^2 + 4X + 2 = 47
}
else if (q == 7) {
override_poly_Q = ""; override_poly = ""; f_hyperoval = FALSE;
}
else if (q == 8) {
override_poly_Q = "97"; override_poly = "11"; f_hyperoval = TRUE;
// F_4096 generated by x^12+x^6+x^4+x+1
// F_64 generated by X^6+X^5+1 = 97
// F_8 generated by X^3+X+1 = 11
}
else if (q == 9) {
override_poly_Q = ""; override_poly = "17"; f_hyperoval = FALSE;
}
make_tensor_code_9_dimensional(q, override_poly_Q, override_poly,
f_hyperoval, code, length, verbose_level - 1);
the_set = NEW_int(length);
int pt[9], rk;
for (t = 0; t < length; t++) {
for (i = 0; i < 9; i++) {
pt[i] = code[i * length + t];
}
F->PG_element_rank_modified(pt, 1, 9, rk);
the_set[t] = rk;
}
FREE_int(code);
if (f_v) {
cout << "make_tensor_code_9dimensional_as_point_set done" << endl;
cout << "created the set: ";
int_vec_print(cout, the_set, length);
cout << endl;
}
}
void coding_theory_domain::create_matrix_H_subfield(
finite_field *F, finite_field*f,
int *H_subfield, int *C, int *C_inv, int *M,
int m, int n, int beta, int beta_q,
int f_elements_exponential, const char *symbol_for_print,
const char *symbol_for_print_subfield,
int f_construction_A, int f_hyperoval, int f_construction_B,
int verbose_level)
{
int f_v = (verbose_level >= 1);
int f_vv = (verbose_level >= 2);
int i, j;
int q;
//int *C;
//int *C_inv;
int *H;
int *AA;
q = f->q;
// matrix C is zero:
H = NEW_int(m * n);
AA = NEW_int(m * m);
for (i = 0; i < m; i++) {
for (j = 0; j < m; j++) {
C[i * m + j] = 0;
}
}
if (f_construction_A) {
int nb_C_coeffs = 15;
int k, aa;
int C_coeffs[] = {
0, 0, 1,
1, 1, 1,
2, 2, 1,
3, 3, 1,
3, 4, 1,
4, 3, beta_q,
4, 4, beta,
5, 5, 1,
5, 6, 1,
6, 5, beta_q,
6, 6, beta,
7, 7, 1,
7, 8, 1,
8, 7, beta_q,
8, 8, beta,
};
for (k = 0; k < nb_C_coeffs; k++) {
i = C_coeffs[k * 3 + 0];
j = C_coeffs[k * 3 + 1];
aa = C_coeffs[k * 3 + 2];
C[i * m + j] = aa;
}
}
else if (f_construction_B) {
int nb_C_coeffs = 20;
int k, aa;
int C_coeffs[] = {
0, 0, 1,
1, 1, 1,
2, 2, 1,
2, 3, 1,
2, 4, 1,
3, 2, beta,
3, 3, beta_q,
3, 4, F->beta_trinomial(q, beta, 1, 0, 0),
4, 2, F->beta_trinomial(q, beta, 0, 0, 2),
4, 3, F->beta_trinomial(q, beta, 0, 2, 0),
4, 4, F->beta_trinomial(q, beta, 2, 0, 0),
5, 5, 1,
5, 6, 1,
5, 7, 1,
6, 5, F->beta_trinomial(q, beta, 0, 1, 1),
6, 6, F->beta_trinomial(q, beta, 1, 1, 0),
6, 7, F->beta_trinomial(q, beta, 1, 0, 1),
7, 5, F->beta_trinomial(q, beta, 0, 2, 2),
7, 6, F->beta_trinomial(q, beta, 2, 2, 0),
7, 7, F->beta_trinomial(q, beta, 2, 0, 2),
};
for (k = 0; k < nb_C_coeffs; k++) {
i = C_coeffs[k * 3 + 0];
j = C_coeffs[k * 3 + 1];
aa = C_coeffs[k * 3 + 2];
C[i * m + j] = aa;
}
}
if (f_v) {
cout << "matrix C:" << endl;
print_integer_matrix_width(cout, C, m, m, m, 2);
F->latex_matrix(cout, f_elements_exponential,
symbol_for_print, C, m, m);
}
F->invert_matrix(C, C_inv, m);
if (f_vv) {
cout << "C_inv:" << endl;
print_integer_matrix_width(cout, C_inv, m, m, m, 2);
}
F->mult_matrix_matrix(C, C_inv, AA, m, m, m,
0 /* verbose_level */);
if (f_vv) {
cout << "C * C_inv:" << endl;
print_integer_matrix_width(cout, AA, m, m, m, 2);
}
F->mult_matrix_matrix(C, M, H, m, m, n,
0 /* verbose_level */);
if (f_v) {
cout << "H = C * M:" << endl;
print_integer_matrix_width(cout, H, m, n, n, 2);
F->latex_matrix(cout, f_elements_exponential,
symbol_for_print, H, m, n);
}
#if 0
rk = F.Gauss_int(M, FALSE /* f_special */, TRUE /* f_complete */, base_cols,
FALSE /* f_P */, NULL, m /* m */, n /* n */, 0 /* Pn */,
verbose_level - 2);
cout << "has rank " << rk << endl;
#endif
tt_field_reduction(*F, *f, m, n, H, H_subfield, verbose_level - 2);
if (f_v) {
cout << "H_subfield:" << endl;
print_integer_matrix_width(cout, H_subfield, m, n, n, 2);
f->latex_matrix(cout, f_elements_exponential,
symbol_for_print_subfield, H_subfield, m, n);
}
FREE_int(H);
FREE_int(AA);
}
void coding_theory_domain::twisted_tensor_product_codes(
int *&H_subfield, int &m, int &n,
finite_field *F, finite_field *f,
int f_construction_A, int f_hyperoval,
int f_construction_B, int verbose_level)
{
int f_v = (verbose_level >= 1);
int f_vv = (verbose_level >= 2);
int index;
int exponents[9];
int *M;
//int *H_subfield;
int *C;
int *C_inv;
int q = f->q;
int q2;
int Q;
//int m, n;
int r;
int beta, beta_q;
int f_elements_exponential = TRUE;
const char *symbol_for_print = "\\alpha";
const char *symbol_for_print_subfield = "\\omega";
if (f_v) {
cout << "twisted_tensor_product_codes" << endl;
cout << "f_construction_A=" << f_construction_A << endl;
cout << "f_hyperoval=" << f_hyperoval << endl;
cout << "f_construction_B=" << f_construction_B << endl;
}
q2 = q * q;
Q = 0;
if (f_construction_A) {
Q = q2;
}
else if (f_construction_B) {
Q = q2 * q;
}
index = (Q - 1) / (q - 1);
if (Q != F->q) {
cout << "twisted_tensor_product_codes Q != F->q" << endl;
exit(1);
}
if (f_vv) {
cout << "q = " << q << endl;
cout << "Q = " << Q << endl;
cout << "index = " << index << endl;
}
#if 0
F.init_override_polynomial(Q, override_poly_Q, verbose_level - 2);
if (f_vv) {
cout << "field of order " << Q << " initialized" << endl;
}
f.init_override_polynomial(q, override_poly_q, verbose_level - 2);
if (f_vv) {
cout << "field of order " << q << " initialized" << endl;
cout << "index = " << index << endl;
}
#endif
F->compute_subfields(verbose_level - 2);
create_matrix_M(
M,
F, f,
m, n, beta, r, exponents,
f_construction_A, f_hyperoval, f_construction_B,
f_elements_exponential, symbol_for_print,
verbose_level - 2);
beta_q = F->power(beta, q);
if (f_vv) {
cout << "twisted_tensor_product_codes after create_matrix_M" << endl;
cout << "m = " << m << endl;
cout << "n = " << n << endl;
cout << "Q = " << Q << endl;
cout << "q2 = " << q2 << endl;
cout << "beta = " << beta << endl;
cout << "beta_q = " << beta_q << endl;
cout << "Exponents: ";
int_vec_print(cout, exponents, m);
cout << endl;
}
if (f_vv) {
cout << "twisted_tensor_product_codes: M:" << endl;
print_integer_matrix_width(cout, M, m, n, n, 2);
F->latex_matrix(cout, f_elements_exponential, symbol_for_print, M, m, n);
}
#if 0
for (j = 0; j < n; j++) {
PG_element_normalize(F, M + j, n, m);
}
cout << "column normalized M:" << endl;
print_integer_matrix_width(cout, M, m, n, n, 2);
#endif
C = NEW_int(m * m);
C_inv = NEW_int(m * m);
H_subfield = NEW_int(m * n);
create_matrix_H_subfield(F, f,
H_subfield, C, C_inv, M, m, n, beta, beta_q,
f_elements_exponential, symbol_for_print, symbol_for_print_subfield,
f_construction_A, f_hyperoval, f_construction_B,
verbose_level - 2);
if (f_v) {
cout << "twisted_tensor_product_codes: after create_matrix_H_subfield" << endl;
cout << "H_subfield:" << endl;
print_integer_matrix_width(cout, H_subfield, m, n, n, 2);
f->latex_matrix(cout, f_elements_exponential, symbol_for_print_subfield, H_subfield, m, n);
}
FREE_int(M);
FREE_int(C);
FREE_int(C_inv);
}
void coding_theory_domain::create_matrix_M(
int *&M,
finite_field *F, finite_field *f,
int &m, int &n, int &beta, int &r, int *exponents,
int f_construction_A, int f_hyperoval, int f_construction_B,
int f_elements_exponential, const char *symbol_for_print,
int verbose_level)
// int exponents[9]
{
int f_v = (verbose_level >= 1);
//int f_vv = (verbose_level >= 2);
int i, j, t, q, Q, q2;
q = f->q;
q2 = q * q;
if (f_construction_A) {
#if 0
//q = 2; override_poly_Q = ""; override_poly = "";
//q = 3; override_poly_Q = ""; override_poly = "";
q = 4; override_poly_Q = "19"; override_poly = "7";
// F_256 generated by X^8 + X^4 + X^3 + X^2 + 1
// F_16 generated by X^4+X+1 = 19
// F_4 generated by X^2+X+1 = 7
//q = 5; override_poly_Q = "47"; override_poly = "";
// F_625 generated by X^4 + X^3 + 3X + 2
// F_25 generated by X^2 + 4X + 2 = 47
//q = 7; override_poly_Q = ""; override_poly = "";
//q = 8; override_poly_Q = "97"; override_poly = "11";
// F_4096 generated by x^12+x^6+x^4+x+1
// F_64 generated by X^6+X^5+1 = 97
// F_8 generated by X^3+X+1 = 11
//q = 9; override_poly_Q = ""; override_poly = "17";
#endif
Q = q2;
beta = q;
m = 9;
if (f_hyperoval) {
n = Q + 2;
}
else {
n = Q + 1;
}
r = 5;
if (q == 4)
r = 7;
if (q == 3)
r = 9;
// 3 orbits of length 1: 0, q+1, 2q+2
exponents[0] = 0;
exponents[1] = q + 1;
exponents[2] = 2 * q + 2;
//orbit (q,1)
exponents[3] = q;
exponents[4] = 1;
// orbit (2q, 2)
exponents[5] = 2 * q;
exponents[6] = 2;
// orbit (2q+1, q+2)
exponents[7] = 2 * q + 1;
exponents[8] = q + 2;
//exponents[0] = 0;
//exponents[1] = q;
//exponents[2] = 2 * q;
//exponents[3] = 1;
//exponents[4] = q + 1;
//exponents[5] = 2 * q + 1;
//exponents[6] = 2;
//exponents[7] = q + 2;
//exponents[8] = 2 * q + 2;
}
else if (f_construction_B) {
#if 0
//q = 2; override_poly_Q = ""; override_poly = ""; r = 9;
//q = 3; override_poly_Q = ""; override_poly = ""; r = 5;
q = 4; override_poly_Q = ""; override_poly = "7"; r = 4;
// F_4096 generated by X^8 + X^4 + X^3 + X^2 + 1 = 4096
//q = 5; override_poly_Q = ""; override_poly = ""; r = 4;
//q = 7; override_poly_Q = ""; override_poly = ""; r = 4;
#endif
beta = q;
Q = q2 * q;
m = 8;
n = Q + 1;
exponents[0] = 0;
exponents[1] = q2 + q + 1;
exponents[2] = 1;
exponents[3] = q;
exponents[4] = q2;
exponents[5] = q + 1;
exponents[6] = q2 + q;
exponents[7] = q2 + 1;
//exponents[0] = 0;
//exponents[1] = q;
//exponents[2] = 1;
//exponents[3] = q + 1;
//exponents[4] = q2;
//exponents[5] = q2 + q;
//exponents[6] = q2 + 1;
//exponents[7] = q2 + q + 1;
}
else {
cout << "create_matrix_M(): please specify the construction using option -A or -B" << endl;
exit(1);
}
// create matrix M:
M = NEW_int(m * n);
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
M[i * n + j] = 0;
}
}
for (t = 0; t < Q; t++) {
for (i = 0; i < m; i++) {
M[i * n + t] = F->power(t, exponents[i]);
}
}
if (f_construction_A) {
M[2 * n + Q] = 1;
if (f_hyperoval)
M[1 * n + Q + 1] = 1;
}
else if (f_construction_B) {
M[1 * n + Q] = 1;
}
if (f_v) {
cout << "M:" << endl;
print_integer_matrix_width(cout, M, m, n, n, 2);
F->latex_matrix(cout, f_elements_exponential,
symbol_for_print, M, m, n);
}
if (f_v) {
int *all_one, *col_sum;
all_one = NEW_int(n);
col_sum = NEW_int(m);
for (i = 0; i < n; i++)
all_one[i] = 1;
F->mult_matrix_matrix(M, all_one, col_sum, m, n, 1,
0 /* verbose_level */);
cout << "overall col_sum:" << endl;
print_integer_matrix_width(cout, col_sum, m, 1, 1, 2);
FREE_int(all_one);
FREE_int(col_sum);
}
}
