lower bound: | 80 |
upper bound: | 82 |
Construction of a linear code [178,13,80] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [168, 11, 76] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^20 + x^18 + x^17 + x^12 + x^11 + 1, x^20 + x^19 + x^18 + x^16 + x^15 + x^14 + x^11 + x^8 + x^7 + x^6 + x + 1, x^18 + x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + x^4 + x^2 + 1, x^20 + x^19 + x^18 + x^16 + x^15 + x^13 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^20 + x^16 + x^15 + x^13 + x^11 + x^10 + x^9 + x^6 + x^5 + x^3 + x^2 + x, x^20 + x^19 + x^18 + x^17 + x^15 + x^13 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^3 + 1, x^20 + x^19 + x^17 + x^16 + x^13 + x^11 + x^9 + x^6 + x^4 + 1, x^19 + x^11 + x^10 + x^9 + x^8 + x^6 + x^4 + x^2 + x + 1 [3]: [168, 11, 76] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^20 + x^18 + x^17 + x^12 + x^11 + 1, x^20 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^4 + x^3, x^19 + x^17 + x^16 + x^15 + x^14 + x^11 + x^9 + x^7 + x^6 + x^3 + x^2 + x, x^19 + x^17 + x^16 + x^14 + x^13 + x^10 + x^8 + x^7 + x^4 + x, x^20 + x^19 + x^18 + x^12 + x^11 + x^7 + x^5 + x^4 + x^2 + 1, x^20 + x^17 + x^16 + x^11 + x^4 + x, x^19 + x^18 + x^16 + x^15 + x^14 + x^13 + x^12 + x^8 + x^5 + x^4 + x^3 + x^2, x^20 + x^17 + x^16 + x^14 + x^13 + x^9 + x^7 + x^6 + x^5 + 1 [4]: [168, 11, 76] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^20 + x^18 + x^17 + x^12 + x^11 + 1, x^18 + x^17 + x^15 + x^13 + x^10 + x^6 + x^5 + x^4 + x^2 + 1, x^20 + x^19 + x^18 + x^16 + x^12 + x^8 + x^7 + x^5 + x + 1, x^20 + x^11 + x^5 + x^2, x^19 + x^17 + x^15 + x^14 + x^9 + x^8 + x^7 + x^6 + x^4 + x^3, x^18 + x^16 + x^15 + x^14 + x^12 + x^9 + x^8 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^20 + x^18 + x^17 + x^15 + x^12 + x^11 + x^10 + x^7 + x^3 + x, x^20 + x^19 + x^18 + x^17 + x^15 + x^14 + x^12 + x^10 + x^5 + x^4 + x^3 + x [5]: [168, 13, 74] Quasicyclic of degree 8 Linear Code over GF(2) The Vector space sum: [4] + [3] [6]: [177, 13, 80] Linear Code over GF(2) Apply ConstructionXChain to [5] [4] [3] [2] and [1] then apply ConstructionXX using [1] [1] [7]: [178, 13, 80] Linear Code over GF(2) ExtendCode [6] by 1 last modified: 2008-11-04
Lb(178,13) = 79 is found by shortening of: Lb(179,14) = 79 is found by truncation of: Lb(180,14) = 80 BZ Ub(178,13) = 82 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
|