lower bound: | 82 |
upper bound: | 88 |
Construction of a linear code [196,17,82] over GF(2): [1]: [9, 1, 9] Cyclic Linear Code over GF(2) RepetitionCode of length 9 [2]: [195, 16, 88] Linear Code over GF(2) QuasiCyclicCode of length 195 stacked to height 3 with generating polynomials: x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^9 + x^8 + x^6 + x^4 + x^3 + x^2 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^11 + x^8 + x^7 + x^3 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1 [3]: [195, 17, 79] Linear Code over GF(2) QuasiCyclicCode of length 195 stacked to height 4 with generating polynomials: x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^9 + x^8 + x^6 + x^4 + x^3 + x^2 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^11 + x^8 + x^7 + x^3 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, 0, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 [4]: [204, 17, 88] Linear Code over GF(2) ConstructionX using [3] [2] and [1] [5]: [195, 17, 82] Linear Code over GF(2) Puncturing of [4] at { 46, 47, 48, 51, 52, 53, 56, 57, 58 } [6]: [196, 17, 82] Linear Code over GF(2) ExtendCode [5] by 1 last modified: 2015-03-10
Lb(196,17) = 80 is found by taking a subcode of: Lb(196,18) = 80 is found by lengthening of: Lb(193,18) = 80 GW2 Ub(196,17) = 88 otherwise adding a parity check bit would contradict: Ub(197,17) = 89 BK
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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