lower bound: | 114 |
upper bound: | 121 |
Construction of a linear code [192,10,114] over GF(3): [1]: [48, 5, 38] Quasicyclic of degree 6 Linear Code over GF(3^2) QuasiCyclicCode of length 48 with generating polynomials: $.1^7*x^7 + $.1^6*x^5 + 2*x^4 + $.1^7*x^3 + x^2 + $.1^3*x + 1, $.1^7*x^7 + $.1*x^6 + $.1^6*x^5 + $.1*x^4 + $.1^6*x^3 + x^2 + $.1^2*x + $.1^7, $.1*x^7 + 2*x^6 + 2*x^5 + $.1*x^4 + $.1^3*x^3 + $.1^7*x + 1, $.1^5*x^7 + $.1^5*x^6 + $.1*x^5 + $.1^3*x^4 + $.1*x^3 + $.1^5*x^2 + 1, $.1*x^7 + $.1^6*x^6 + $.1^6*x^5 + $.1^7*x^3 + $.1^5*x^2 + $.1^5*x, x^7 + $.1*x^6 + $.1^3*x^5 + $.1^6*x^4 + $.1^5*x^3 + $.1^7*x^2 + $.1^2*x + 1 [2]: [121, 116, 3] "Hamming code (r = 5)" Linear Code over GF(3) 5-th order HammingCode over GF( 3) [3]: [121, 5, 81] Cyclic Linear Code over GF(3) Dual of [2] [4]: [119, 5, 79] Linear Code over GF(3) Puncturing of [3] at { 120 .. 121 } [5]: [40, 4, 27] Linear Code over GF(3) ResidueCode of [4] [6]: [38, 4, 25] Linear Code over GF(3) Puncturing of [5] at { 39 .. 40 } [7]: [13, 3, 9] Linear Code over GF(3) ResidueCode of [6] [8]: [11, 3, 7] Linear Code over GF(3) Puncturing of [7] at { 12 .. 13 } [9]: [4, 2, 3] Linear Code over GF(3) ResidueCode of [8] [10]: [192, 10, 114] Linear Code over GF(3) ZinovievCode using inner codes: [9], outer codes: [1] last modified: 2003-10-31
Lb(192,10) = 114 BZ Ub(192,10) = 121 Da2
Da2: R.N. Daskalov, The linear programming bound for ternary linear codes, p. 423 in: IEEE International Symposium on Information Theory, Trondheim, 1994.
Notes
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