lower bound: | 75 |
upper bound: | 81 |
Construction of a linear code [135,12,75] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [132, 11, 73] Quasicyclic of degree 12 Linear Code over GF(3) QuasiCyclicCode of length 132 with generating polynomials: x^3, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^4 + x^2 + 2*x, 2*x^6 + 2*x^5 + x^3 + x, 2*x^10 + x^8 + x^7 + 2*x^6 + x^3 + x^2 + 2*x + 2, x^9 + x^8 + 2*x^5 + x^4 + x^2 + 2, x^10 + x^9 + x^6 + 2*x^5 + 2*x^3 + x^2 + 2, 2*x^10 + 2*x^9 + 2*x^7 + x^6 + x^5 + 2*x^3 + 2*x^2, 2*x^10 + x^8 + x^7 + x^5 + 2*x^4 + x^3 + 2*x + 2, x^9 + x^8 + x^7 + x^6 + 2*x^5 + x^4 + x + 2, 2*x^10 + x^9 + x^8 + x^7 + 2*x^6 + x^2 + x + 1, 2*x^10 + x^9 + x^8 + x^7 + 2*x^5 + 2*x^4 + 2*x^2, x^10 + 2*x^8 + x^7 + 2*x^6 + x^4 + x^3 + 2*x^2 + 2*x + 1 [3]: [132, 11, 73] Quasicyclic of degree 12 Linear Code over GF(3) QuasiCyclicCode of length 132 with generating polynomials: x^8, 2*x^9 + x^7 + 2*x^6 + 2*x^4 + 2*x^3 + 2*x^2, x^10 + 2*x^9 + 2*x^7 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1, 2*x^10 + 2*x^9 + x^6 + x^5 + x^4 + 2*x^3 + 1, x^10 + 2*x^8 + 2*x^6 + x^5 + 2*x^4 + 2*x + 2, x^9 + 2*x^7 + x^6 + 2*x^4 + 2*x^3 + x^2 + x + 2, 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + x, 2*x^10 + 2*x^8 + x^7 + x^3 + 2*x^2 + 2*x + 1, 2*x^10 + x^9 + x^6 + 2*x^5 + x^3 + x^2 + x + 1, x^7 + x^6 + x^5 + 2*x^4 + x^3 + x^2 + x + 2, x^10 + x^9 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2, x^10 + 2*x^9 + 2*x^8 + 2*x^5 + 2*x^4 + x^3 + 2*x [4]: [132, 11, 73] Quasicyclic of degree 12 Linear Code over GF(3) QuasiCyclicCode of length 132 with generating polynomials: 2*x^10 + 1, x^10 + x^9 + x^8 + 2*x^7 + x^4 + 2*x + 1, x^10 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x^2, 2*x^10 + 2*x^8 + 2*x^7 + 2*x^4 + 2*x, x^9 + x^8 + 2*x^5 + x^4 + 2*x^3 + x^2 + x + 1, x^6 + x^4 + 2*x^3 + 2*x^2 + 2*x, 2*x^10 + 2*x^8 + x^7 + 2*x^6 + x^4 + x^3 + 2*x^2 + x + 1, x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^2 + 2*x, x^9 + x^8 + x^7 + x^6 + x^2 + 2*x + 2, x^10 + x^7 + 2*x^6 + x^3 + x^2, x^10 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + 2*x, 2*x^10 + x^9 + x^7 + 2*x^3 + 2*x^2 + 2*x + 1 [5]: [132, 12, 72] Linear Code over GF(3) QuasiCyclicCode of length 132 stacked to height 2 with generating polynomials: 0, 0, x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2, x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 0, 0, x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2, x^8, 2*x^9 + x^7 + 2*x^6 + 2*x^4 + 2*x^3 + 2*x^2, x^10 + 2*x^9 + 2*x^7 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1, 2*x^10 + 2*x^9 + x^6 + x^5 + x^4 + 2*x^3 + 1, x^10 + 2*x^8 + 2*x^6 + x^5 + 2*x^4 + 2*x + 2, x^9 + 2*x^7 + x^6 + 2*x^4 + 2*x^3 + x^2 + x + 2, 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + x, 2*x^10 + 2*x^8 + x^7 + x^3 + 2*x^2 + 2*x + 1, 2*x^10 + x^9 + x^6 + 2*x^5 + x^3 + x^2 + x + 1, x^7 + x^6 + x^5 + 2*x^4 + x^3 + x^2 + x + 2, x^10 + x^9 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2, x^10 + 2*x^9 + 2*x^8 + 2*x^5 + 2*x^4 + x^3 + 2*x [6]: [135, 12, 75] Linear Code over GF(3) Apply ConstructionXChain to [5] [4] [3] [2] and [1] then apply ConstructionXX using [1] [1] last modified: 2010-01-04
Lb(135,12) = 72 is found by taking a subcode of: Lb(135,13) = 72 BZ Ub(135,12) = 81 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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