bool symmetry_group_walker::nextsub (int g) {
bool of = next_perm (perms[g]);
if (of && g > 0)
of = nextsub (g - 1);
return of;
}
static int weight_of_linear_combinations(MINDIST *MD, int l)
//evaluate minimum-weight of all codevectors that are constructed
//by linearcombinations of $l$ rows of matrix $S[1],...,S[M]$
//algorithm: create all possibilities for combining $l$ rows out of $k$
//possible matrix rows by constructing the $l$-element-
//subsets over $\{1,...,k\}$;
//create all possibilities for filling an $l$-element-subset by
//$\{1,...,p\}$ while construct the p-adic numbers of $0,...,lc$
//($lc$ = number of possibilities for filling);
//combining the two results gives all possibilities of linear-
//combinations of $l$ matrix-rows;
//out of this construct the codevectors and
//calculate minimumweight
//$l$ = \# rows taken for linearcombination
// needed: weight(int *p, n, idx\_zero)
{
int n = MD->n;
int k = MD->k;
int q = MD->q;
int M = MD->M;
int d1;
int d_l; /* minimum-weight by combining l rows */
int lc, dec, h;
int i, j, z, w;
int *v,*linc,*lcv;
int *sub;
/* for l = 1 the weight of a multiple of a generating codevector
is equal to the weight of that codevector (p = prim) */
/* allocate array for l-subset of a k-set */
sub = (int *)calloc(k+1,sizeof (int));
d_l = n;
if (l == 1) {
for (z=1;z<=M;z++) {
for (i=1;i<=k;i++) {
if (MD->Size[z] > 0) {
d1 = weight(MD->S[z][i], n, MD->idx_zero);
MD->weight_computations++;
if (d1 > 0) {
d_l = MINIMUM(d_l,d1);
if (MD->f_vv) {
cout << "matrix " << z << " row " << i << " is ";
for (j=1;j <=n;j++) cout << MD->S[z][i][j] << " ";
cout << " of weight " << d1 << " minimum is " << d_l << endl;
}
}
} // if
} // next z
} // next i
free(sub);
return(d_l);
}
/* construct codevectors by linear combinations of l rows
of the generator matrices and calculate their weight */
else {
/* allocate memory for help-pointers */
v = (int*)calloc(l+2,sizeof(int));
linc = (int*)calloc(k+2,sizeof(int));
lcv = (int*)calloc(n+2,sizeof(int));
lc = i_power_j(q-1, l);
#if 0
lc = expo(p-1,l); /* number of possibilities to replace one
* subset with entries 1,...,p-1 */
#endif
/* If the l-subset is b_1,...,b_l, then form the
linear combination of the rows b_i times v[i] */
for (dec = 1; dec <= lc; dec++) {
padic(dec, v, l, q-1);
/* for each systematic-generator-matrix S[z] */
for (z=1;z<=M;z++) {
int K = MD->Size[z];
if (K<l)
continue;
/* initialize with set: 1,2,...,l */
for (i=1;i<=l;i++)
sub[i] = i;
/* for (i=1;i<=l;i++)
printf("%d ",sub[i]); printf("\n"); */
do {
/* for (i=1;i<=l;i++) printf("%d ",sub[i]); */
h = 1;
for (j=1;j<=K;j++) {
if (j == sub[h]) {
linc[j] = v[h-1]+1;
if (h != l)
h = h+1;
} /* if */
else
linc[j] = 0;
} /* j */
/* construct the corresponding codevector lcv */
vmmult(MD, linc, MD->S[z], lcv);
/* calculate its weight and store if minimal */
w = weight(lcv, n, MD->idx_zero);
MD->weight_computations++;
d_l = MINIMUM(d_l,w);
if (MD->f_vv) {
for (i=1;i <=k;i++) cout << linc[i] << " ";
cout << " : ";
for (i=1;i <=n;i++) cout << lcv[i] << " ";
cout << " of weight " << w << " minimum is " << d_l << endl;
}
} while (nextsub(K,l,sub)); /* next l-subset of K-set */
} /* z */
} /* dec */
free(v);
free(linc);
free(lcv);
free(sub);
return(d_l);
} /* else */
}
