create_BCH_code.cpp

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/*
 * create_BCH_code.cpp
 *
 *  Created on: Jan 13, 2022
 *      Author: betten
 */
 
 
 
#include "foundations.h"
 
using namespace std;
 
 
 
namespace orbiter {
namespace layer1_foundations {
namespace coding_theory {
 
create_BCH_code::create_BCH_code()
{
    n = 0;
    d = 0;
    F = NULL;
 
    Nth = NULL;
 
    P = NULL;
 
    Selection = NULL;
    Sel = NULL;
    nb_sel = 0;
 
    degree = 0;
    k = 0;
    Genma = NULL;
    generator_polynomial = NULL;
}
 
create_BCH_code::~create_BCH_code()
{
}
 
void create_BCH_code::init(field_theory::finite_field *F, int n, int d, int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "create_BCH_code::init" << endl;
    }
 
    coding_theory_domain Codes;
 
    create_BCH_code::n = n;
    create_BCH_code::d = d;
    create_BCH_code::F = F;
 
    Nth = NEW_OBJECT(field_theory::nth_roots);
 
    Nth->init(F, n, verbose_level);
 
    int i, j;
 
 
    Selection = NEW_int(Nth->Cyc->S->nb_sets);
    Sel = NEW_int(Nth->Cyc->S->nb_sets);
 
    for (i = 0; i < Nth->Cyc->S->nb_sets; i++) {
        Selection[i] = FALSE;
    }
 
    for (i = 0; i < d - 1; i++) {
        j = Nth->Cyc->Index[(1 + i) % n];
        Selection[j] = TRUE;
    }
 
    nb_sel = 0;
    for (i = 0; i < Nth->Cyc->S->nb_sets; i++) {
        if (Selection[i]) {
            Sel[nb_sel++] = i;
        }
    }
 
    if (f_v) {
        cout << "coding_theory_domain::make_BCH_code Sel=";
        Int_vec_print(cout, Sel, nb_sel);
        cout << endl;
    }
 
    ring_theory::unipoly_object Q;
 
    P = NEW_OBJECT(ring_theory::unipoly_object);
    Nth->FX->create_object_by_rank(*P, 1, __FILE__, __LINE__, 0 /*verbose_level*/);
    Nth->FX->create_object_by_rank(Q, 1, __FILE__, __LINE__, 0 /*verbose_level*/);
 
    for (i = 0; i < nb_sel; i++) {
 
        j = Sel[i];
 
        if (f_v) {
            cout << "coding_theory_domain::make_BCH_code P=";
            Nth->FX->print_object(*P, cout);
            cout << endl;
            cout << "j=" << j << endl;
            Nth->FX->print_object(Nth->generator_Fq[j], cout);
            cout << endl;
        }
        Nth->FX->mult(*P, Nth->generator_Fq[j], Q, verbose_level);
        if (f_v) {
            cout << "coding_theory_domain::make_BCH_code Q=";
            Nth->FX->print_object(Q, cout);
            cout << endl;
        }
        Nth->FX->assign(Q, *P, 0 /* verbose_level */);
    }
 
 
    degree = Nth->FX->degree(*P);
    generator_polynomial = NEW_int(degree + 1);
    for (i = 0; i <= degree; i++) {
        generator_polynomial[i] = Nth->FX->s_i(*P, i);
    }
 
    Codes.generator_matrix_cyclic_code(n,
                degree, generator_polynomial, Genma);
 
    k = n - degree;
 
 
    if (f_v) {
        cout << "create_BCH_code::init done" << endl;
    }
}
 
 
void create_BCH_code::report(std::ostream &ost, int verbose_level)
{
    int f_v = (verbose_level >= 1);
    int i;
    string label;
    coding_theory_domain Codes;
    orbiter_kernel_system::latex_interface Li;
 
    if (f_v) {
        cout << "create_BCH_code::report" << endl;
    }
 
 
    ost << "\\noindent" << endl;
    ost << "BCH-code:\\\\" << endl;
    ost << "$n=" << n << ",$ $k=" << k << ",$ $d_0=" << d << ",$ $q=" << F->q << ",$ \\\\" << endl;
    ost << "$g(x) = ";
    for (i = 0; i < nb_sel; i++) {
        ost << "m_{" << Sel[i] << "}";
    }
    ost << "=" << endl;
    //ost << "$" << endl;
    Nth->FX->print_object(*P, ost);
    ost << "$" << endl;
    ost << "\\\\" << endl;
 
 
    ost << "\\noindent" << endl;
    ost << "Chosen cyclotomic sets:\\\\" << endl;
    Nth->Cyc->print_latex_with_selection(ost, Sel, nb_sel);
 
    ost << "\\bigskip" << endl;
 
 
    ost << "The generator polynomial has degree " << degree << endl;
 
    ost << "\\begin{verbatim}" << endl;
    ost << "-dense \"";
    Nth->FX->print_object_dense(*P, ost);
    ost << "\"" << endl;
    ost << endl;
 
    ost << "-sparse \"";
    Nth->FX->print_object_sparse(*P, ost);
    ost << "\"" << endl;
    ost << endl;
    ost << "\\end{verbatim}" << endl;
 
 
    if (n < 22) {
 
        ost << "The generator matrix is:" << endl;
        ost << "$$" << endl;
        ost << "\\left[" << endl;
        Li.int_matrix_print_tex(ost, Genma, k, n);
        ost << "\\right]" << endl;
        ost << "$$" << endl;
 
    }
 
    if (f_v) {
        cout << "create_BCH_code::report done" << endl;
    }
}
 
}}}