[b093b0] | 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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