lower bound: | 80 |
upper bound: | 82 |
Construction of a linear code [176,12,80] over GF(2): [1]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [2]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [3]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [2] and [1] [4]: [7, 3, 4] Linear Code over GF(2) Shortening of [3] at 1 [5]: [168, 9, 80] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^18 + x^15 + x^9 + 1, x^18 + x^15 + x^14 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^2 + x + 1, x^18 + x^15 + x^13 + x^10 + x^9 + x^7 + x + 1, x^18 + x^16 + x^15 + x^12 + x^7 + x^6 + x^4 + x, x^20 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^11 + x^10 + x^6 + x^4 + x^2, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^2 + x + 1, x^20 + x^19 + x^18 + x^17 + x^15 + x^11 + x^10 + x^9 + x^7 + x^4 + x^2 + 1, x^20 + x^17 + x^16 + x^15 + x^14 + x^13 + x^10 + x^8 + x^6 + x^4 + x^3 + 1 [6]: [168, 12, 76] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^15 + x^12 + 1, x^20 + x^18 + x^17 + x^13 + x^11 + x^9 + x^7 + x^6 + x^4 + x^3 + x^2, x^19 + x^18 + x^16 + x^10 + x^9 + x^6 + x^3 + x, x^20 + x^18 + x^17 + x^16 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^5 + x^4 + x^2, x^20 + x^16 + x^15 + x^11 + x^10 + x^8 + x^7 + x^6 + x^5 + x^3 + 1, x^14 + x^13 + x^12 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3, x^20 + x^15 + x^12 + x^11 + x^10 + x^8 + x^5 + x^4 + x + 1, x^20 + x^19 + x^18 + x^14 + x^13 + x^11 + x^6 + x^4 + x + 1 [7]: [175, 12, 80] Linear Code over GF(2) ConstructionX using [6] [5] and [4] [8]: [176, 12, 80] Linear Code over GF(2) ExtendCode [7] by 1 last modified: 2003-04-02
Lb(176,12) = 80 is found by lengthening of: Lb(175,12) = 80 GW2 Ub(176,12) = 82 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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