lower bound: | 75 |
upper bound: | 78 |
Construction of a linear code [170,13,75] 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^16 + x^14 + x^13 + x^11 + x, x^20 + x^18 + x^16 + x^15 + x^14 + x^9 + x^7 + x^5 + x^4 + x^2 + x + 1, x^17 + x^14 + x^13 + x^12 + x^10 + x^7 + x^6 + x^3 + x^2 + x, x^18 + x^16 + x^14 + x^13 + x^10 + x^8 + x^6 + x^5 + x^4 + 1, x^20 + x^17 + x^15 + x^14 + x^13 + x^12 + x^10 + x^9 + x^8 + x^7 + x^3 + x, x^15 + x^14 + x^10 + x^8 + x^6 + x^5 + x^4 + x^3 + x + 1, x^19 + x^16 + x^14 + x^8 + x^5 + x^4, x^19 + x^18 + x^16 + x^15 + x^11 + x^9 + x^5 + x^4 + x^2 + 1 [3]: [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 [4]: [171, 13, 76] Linear Code over GF(2) ConstructionX using [3] [2] and [1] [5]: [170, 13, 75] Linear Code over GF(2) Puncturing of [4] at { 171 } last modified: 2008-11-04
Lb(170,13) = 74 is found by shortening of: Lb(171,14) = 74 BZ Ub(170,13) = 78 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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