lower bound: | 64 |
upper bound: | 66 |
Construction of a linear code [140,10,64] over GF(2): [1]: [140, 11, 64] Linear Code over GF(2) QuasiCyclicCode of length 140 stacked to height 3 with generating polynomials: x^6 + x^5 + x^4 + x, x^6 + x^4 + x^3 + x^2, x^6 + x^3 + x + 1, x^6 + x^5 + x^2 + 1, x^5 + x^3 + x^2 + x, x^4 + x^2 + x + 1, x^6 + x^3 + x + 1, x^6 + x^5 + x^4 + x, x^5 + x^3 + x^2 + x, x^4 + x^2 + x + 1, 0, x^4 + x^2 + x + 1, 0, 0, x^6 + x^4 + x^3 + x^2, x^5 + x^3 + x^2 + x, x^6 + x^3 + x + 1, 0, x^6 + x^3 + x + 1, x^6 + x^5 + x^2 + 1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^6 + x^5 + x^3, x^6 + x^2 + x, x^6 + x^4 + x^3 + x^2, x^6 + x^3 + x + 1, 0, x^6 + x^4 + x^3 + x^2, x^5 + x^4 + x^3 + 1, x^5 + x^4 + x^3 + 1, x^6 + x^5 + x^3, x^6 + x^4 + 1, x^6 + x^4 + 1, 0, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^4 + x^3 + x, x^6 + x^5 + x^3, x^6 + x^4 + 1, x^6 + x^5 + x^2 + 1, x^6 + x^3 + x + 1, x^6 + x^3 + x + 1, x^6 + x^4 + 1, x^5 + x^4 + x^2, x^6 + x^4 + 1, x^6 + x^5 + x^3, x^4 + x^3 + x, x^3 + x^2 + 1, x^5 + x^4 + x^2, x^6 + x^5 + x^3, x^6 + x^4 + 1, x^5 + x + 1, x^6 + x^5 + x^3, x^6 + x^2 + x, x^5 + x + 1, x^4 + x^2 + x + 1, x^6 + x^4 + x^3 + x^2, x^6 + x^5 + x^4 + x, x^6 + x^3 + x + 1, x^3 + x^2 + 1, x^6 + x^4 + 1, x^6 + x^4 + 1 [2]: [140, 10, 64] Linear Code over GF(2) Subcode of [1] last modified: 2007-03-22
Lb(140,10) = 64 is found by shortening of: Lb(141,11) = 64 is found by adding a parity check bit to: Lb(140,11) = 63 GB6 Ub(140,10) = 66 follows by a one-step Griesmer bound from: Ub(73,9) = 32 follows by a one-step Griesmer bound from: Ub(40,8) = 16 otherwise adding a parity check bit would contradict: Ub(41,8) = 17 BJV
GB6: T. A. Gulliver & V. K. Bhargava, Improvements to the bounds on optimal binary linear codes of dimensions 11 and 12, Ars Combinatoria 44 (1996) 173-181.
Notes
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