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::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 action_on_bricks::compute_image_linear_action(INT *Elt, INT i, INT &j, INT verbose_level)
{
//verbose_level = 3; // !!!
INT f_v = (verbose_level >= 1);
//INT f_vv = (verbose_level >= 2);
INT v[3], w[3], rk_v, rk_w;
INT vv[3], ww[3], rk_vv, rk_ww;
if (f_v) {
cout << "action_on_bricks::compute_image i = " << i << endl;
}
if (i < 0 || i >= degree) {
cout << "action_on_bricks::compute_image i = " << i << " out of range" << endl;
exit(1);
}
B->unrank_coordinates(i, v[0], v[1], w[0], w[1], 0);
v[2] = 1;
w[2] = 1;
if (f_v) {
cout << "action_on_bricks::compute_image v=";
INT_vec_print(cout, v, 3);
cout << endl;
cout << "action_on_bricks::compute_image w=";
INT_vec_print(cout, w, 3);
cout << endl;
}
PG_element_rank_modified(*B->F, v, 1, 3, rk_v);
PG_element_rank_modified(*B->F, w, 1, 3, rk_w);
if (f_v) {
cout << "action_on_bricks::compute_image rk_v=" << rk_v << endl;
cout << "action_on_bricks::compute_image rk_w=" << rk_w << endl;
cout << "action_on_bricks::compute_image A=" << endl;
A->element_print_quick(Elt, cout);
}
rk_vv = A->image_of(Elt, rk_v);
rk_ww = A->image_of(Elt, rk_w);
if (f_v) {
cout << "action_on_bricks::compute_image rk_vv=" << rk_vv << endl;
cout << "action_on_bricks::compute_image rk_ww=" << rk_ww << endl;
}
PG_element_unrank_modified(*B->F, vv, 1, 3, rk_vv);
PG_element_unrank_modified(*B->F, ww, 1, 3, rk_ww);
if (f_v) {
cout << "action_on_bricks::compute_image vv=";
INT_vec_print(cout, vv, 3);
cout << endl;
cout << "action_on_bricks::compute_image ww=";
INT_vec_print(cout, ww, 3);
cout << endl;
}
if (vv[2] == 0) {
cout << "action_on_bricks::compute_image vv[2] == 0" << endl;
exit(1);
}
if (ww[2] == 0) {
cout << "action_on_bricks::compute_image ww[2] == 0" << endl;
exit(1);
}
PG_element_normalize(*B->F, vv, 1, 3);
PG_element_normalize(*B->F, ww, 1, 3);
if (f_v) {
cout << "action_on_bricks::compute_image after normalize vv=";
INT_vec_print(cout, vv, 3);
cout << endl;
cout << "action_on_bricks::compute_image after normalize ww=";
INT_vec_print(cout, ww, 3);
cout << endl;
}
j = B->rank_coordinates(vv[0], vv[1], ww[0], ww[1], 0);
if (j < 0 || j >= degree) {
cout << "action_on_bricks::compute_image j = " << j << " out of range" << endl;
exit(1);
}
}
