lower bound: | 91 |
upper bound: | 99 |
Construction of a linear code [162,12,91] over GF(3): [1]: [3, 1, 3] Cyclic Linear Code over GF(3) RepetitionCode of length 3 [2]: [161, 11, 93] Quasicyclic of degree 7 Linear Code over GF(3) QuasiCyclicCode of length 161 with generating polynomials: 2*x^22 + 2*x^21 + x^20 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + 2*x^12 + x^6, x^17 + 2*x^12 + 2*x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^2 + 2*x + 1, x^22 + x^19 + 2*x^16 + 2*x^15 + x^14 + x^13 + x^10 + x^8 + 2*x^6 + x^4 + x^3 + 1, x^20 + 2*x^19 + x^16 + x^15 + 2*x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + 2*x^3 + 2*x + 1, 2*x^22 + x^21 + 2*x^20 + x^18 + 2*x^17 + x^16 + 2*x^12 + 2*x^11 + 2*x^9 + x^8 + x^6 + x^4 + 2*x^3 + 2*x^2 + 2, x^22 + x^20 + 2*x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + 2*x^11 + 2*x^9 + 2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^4 + x^2 + 2*x + 1, x^21 + 2*x^20 + 2*x^19 + 2*x^18 + x^17 + x^16 + 2*x^13 + x^12 + x^10 + 2*x^9 + 2*x^6 + 2*x^5 + x^3 + 2*x^2 + 2*x [3]: [161, 12, 90] Quasicyclic of degree 7 Linear Code over GF(3) QuasiCyclicCode of length 161 with generating polynomials: 2*x^22 + 2*x^21 + 2*x^20 + 2*x^17 + x^15 + 2*x^14 + 2*x^13 + x^8, x^22 + 2*x^21 + x^20 + x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^14 + x^13 + 2*x^12 + 2*x^9 + 2*x^5 + x^4 + 2*x^2, 2*x^22 + 2*x^21 + 2*x^20 + 2*x^19 + x^18 + 2*x^17 + x^15 + 2*x^14 + x^13 + x^12 + x^9 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + x, x^20 + x^19 + x^14 + x^13 + 2*x^12 + 2*x^10 + x^9 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^2 + x + 2, 2*x^22 + x^21 + x^19 + x^17 + x^14 + x^13 + x^11 + 2*x^9 + 2*x^8 + x^7 + 2*x^4 + x^3 + 2*x^2 + 2, 2*x^21 + x^20 + x^19 + 2*x^18 + 2*x^17 + x^15 + 2*x^14 + 2*x^13 + x^11 + 2*x^10 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 1, x^22 + 2*x^21 + 2*x^20 + 2*x^19 + x^18 + 2*x^14 + 2*x^13 + 2*x^12 + x^11 + x^10 + 2*x^7 + 2*x^5 + x^3 + 2*x^2 + x [4]: [164, 12, 93] Linear Code over GF(3) ConstructionX using [3] [2] and [1] [5]: [162, 12, 91] Linear Code over GF(3) Puncturing of [4] at { 163 .. 164 } last modified: 2010-02-16
Lb(162,12) = 90 is found by taking a subcode of: Lb(162,13) = 90 BZ Ub(162,12) = 99 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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