1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | // used more arry entries(length(w)) than allocated(var(R)) |
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5 | LIB "decodegb.lib"; |
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6 | |
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7 | int q=16; // square root of the finite field size |
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8 | int k,j,l; |
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9 | //importfrom(Top, q); |
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10 | int nr_transmission=100; |
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11 | int max_weight; // maximum weight of functions used for code construction |
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12 | |
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13 | ring r0=(2^8,a),(e2,e1,x),(wp(1+0,1,1)); |
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14 | |
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15 | ideal monomials = kbase(std(ideal(x^(q^2)-x, e1, e2))); |
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16 | intvec sort_result = sortvec(monomials); |
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17 | intvec monomial_weights = 0:size(monomials); |
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18 | ideal sorted_monomials; |
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19 | for (k=1; k <= size(monomials); k++) { |
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20 | sorted_monomials[k] = monomials[sort_result[k]]; |
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21 | monomial_weights[k] = deg(sorted_monomials[k]); |
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22 | } |
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23 | |
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24 | list all_field_elements = 0; |
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25 | for (j=0; j<=q^2-2; j++) { |
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26 | all_field_elements = all_field_elements + list(a^j); |
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27 | }; |
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28 | |
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29 | |
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30 | matrix generator_matrix[size(sorted_monomials)][size(sorted_monomials)]; |
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31 | for (j=1; j<=size(sorted_monomials); j++) { |
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32 | for (k=1; k<=size(sorted_monomials); k++) { |
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33 | generator_matrix[j,k] = subst(sorted_monomials[j], x, all_field_elements[k]); |
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34 | } |
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35 | } |
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36 | matrix inv_generator_matrix = inverse(generator_matrix); |
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37 | |
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38 | max_weight=254; |
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39 | ring r=(2^8,a),(e2,e1,x),(wp(1+max_weight,1,1)); |
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40 | |
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41 | ideal sorted_monomials = imap(r0, sorted_monomials); |
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42 | int found_monomial=0; |
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43 | for (j=1; j<=size(sorted_monomials); j++) { |
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44 | if (max_weight == deg(sorted_monomials[j])) { |
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45 | found_monomial=1; |
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46 | } |
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47 | } |
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48 | if (!found_monomial) { max_weight--; continue; } |
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49 | |
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50 | int minimum_distance = size(sorted_monomials)-max_weight+1; |
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51 | int correctable_errors = (minimum_distance-1) div 2; |
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52 | list all_curve_points = imap(r0, all_field_elements); |
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53 | matrix generator_matrix = imap(r0, generator_matrix); |
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54 | matrix inv_generator_matrix = imap(r0, inv_generator_matrix); |
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55 | int error_modifier, counter; |
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56 | error_modifier=0; |
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57 | int nr_errors = correctable_errors + error_modifier; |
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58 | counter=1; |
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59 | // Randomly generate information. |
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60 | //printf("counter=%s", counter); |
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61 | matrix info[1][size(sorted_monomials)]; |
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62 | for (k=1; k<=size(sorted_monomials); k++) { |
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63 | if (deg(sorted_monomials[k]) <= max_weight /* *(counter mod 3) div 2 */ ) { |
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64 | info[1,k] = a^(random(0,q^2-2)); |
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65 | } else { |
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66 | info[1,k] = 0; |
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67 | } |
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68 | } |
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69 | matrix codeword = encode(info, generator_matrix); |
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70 | matrix recvword = errorRand(codeword, nr_errors, 8); |
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71 | matrix recv_info = recvword * inv_generator_matrix; |
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72 | matrix zero_mask[1][size(sorted_monomials)]; |
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73 | for (j=1; j<= size(sorted_monomials); j++) { |
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74 | if ((recvword-codeword)[j]==0) { |
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75 | zero_mask[1,j] = 1; |
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76 | } else { |
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77 | zero_mask[1,j] = 0; |
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78 | } |
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79 | } |
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80 | matrix zero_mask_info = zero_mask * inv_generator_matrix; |
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81 | poly info_poly = (info * matrix(sorted_monomials, size(sorted_monomials),1))[1,1]; |
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82 | poly interpolation_polynomial = (recv_info * matrix(sorted_monomials, size(sorted_monomials),1))[1,1]; |
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83 | poly zero_mask_polynomial = (zero_mask_info * matrix(sorted_monomials, size(sorted_monomials),1))[1,1]; |
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84 | poly min_zero_mask_poly = groebner(ideal(zero_mask_polynomial,x^(q^2)-x))[1]; |
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85 | |
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86 | ideal gb = groebner(ideal(e1*(x^(q^2)-x), -e2+e1*interpolation_polynomial)); |
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87 | poly min_degree_poly_with_lpos_two; |
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88 | for (j=1; j<=size(gb); j++) { |
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89 | if (deg(lead(gb[j]), intvec(1,0,0,0)) == 1) { |
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90 | min_degree_poly_with_lpos_two = gb[j]; |
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91 | break; |
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92 | } |
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93 | } |
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94 | poly target_poly = e1*info_poly*min_zero_mask_poly-e2*min_zero_mask_poly; |
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95 | |
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96 | //ideal(min_degree_poly_with_lpos_two); |
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97 | division(target_poly, ideal(min_degree_poly_with_lpos_two)); |
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98 | |
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99 | tst_status(1);$ |
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