lower bound: | 78 |
upper bound: | 80 |
Construction of a linear code [174,13,78] 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^15 + x^14 + x^11 + x^3, x^20 + x^19 + x^16 + x^15 + x^13 + x^10 + x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + x + 1, x^20 + x^15 + x^14 + x^11 + x^9 + x^6, x^20 + x^19 + x^18 + x^16 + x^14 + x^10 + x^9 + x^6 + x^5 + x^3 + x^2 + x, x^17 + x^14 + x^10 + x^4 + x^2 + x, x^20 + x^19 + x^15 + x^13 + x^12 + x^11 + x^10 + x^8 + x^5 + 1, x^16 + x^15 + x^14 + x^13 + x^12 + x^9 + x^8 + x^5 + x^3 + x, x^19 + x^18 + x^16 + x^14 + x^13 + x^12 + x^11 + x^8 + x^7 + x^3 + x^2 + 1 [3]: [168, 11, 76] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^20 + x^16 + x^14 + x^13 + x^11 + x, x^17 + x^16 + x^12 + x^11 + x^8 + x^7 + x^6 + x^4 + x^3 + x, x^20 + x^18 + x^15 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^5 + x + 1, x^20 + x^19 + x^18 + x^17 + x^11 + x^7 + x^6 + x^2 + x + 1, x^18 + x^13 + x^11 + x^10 + x^7 + x^6 + x^5 + x^2 + x + 1, x^20 + x^18 + x^17 + x^12 + x^11 + x^10 + x^9 + x^4 + x^2 + x, x^20 + x^17 + x^13 + x^11 + x^10 + x^7 + x^2 + x, x^13 + x^12 + x^11 + x^10 + x^7 + x^6 + x^5 + x^3 + x^2 + x [4]: [168, 13, 74] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 stacked to height 2 with generating polynomials: x^20 + x^18 + x^14 + x^12 + x^11 + x^9, x^18 + x^17 + x^12 + x^11 + x^10 + x^8 + x^4 + x^3 + x + 1, x^19 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^7 + x^2 + 1, x^18 + x^15 + x^14 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^2 + x + 1, x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^6 + x^4 + x^2, x^17 + x^16 + x^14 + x^12 + x^11 + x^10 + x^7 + x^6 + x^5 + x^3, x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^10 + x^9 + x^7 + x^4 + x^2 + x + 1, x^20 + x^19 + x^18 + x^16 + x^15 + x^13 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5, x^20 + x^19 + x^14 + x^13 + x^11 + x^9 + x^4 + x^3 + x + 1, x^17 + x^14 + x^12 + x^11 + x^10 + x^6 + x^5 + x^4 + x^3 + x, x^17 + x^16 + x^15 + x^13 + x^12 + x^10 + x^9 + x^8 + x^5 + x^4 + x^3 + x^2, x^19 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^10 + x^9 + x^7 + x^4 + x^3 + x^2 + x, x^15 + x^10 + x^9 + x^6 + x^4 + x, x^20 + x^16 + x^13 + x^12 + x^9 + x^8 + x^6 + x^2 + x + 1, x^19 + x^16 + x^10 + x, x^20 + x^16 + x^14 + x^13 + x^9 + x^5 + x^3 + x^2 + x + 1 [5]: [174, 13, 78] Linear Code over GF(2) ConstructionXX using [4] [3] [2] [1] and [1] last modified: 2008-11-04
Lb(174,13) = 76 is found by taking a subcode of: Lb(174,14) = 76 BZ Ub(174,13) = 80 is found by considering shortening to: Ub(173,12) = 80 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
|