lower bound: | 120 |
upper bound: | 122 |
Construction of a linear code [252,11,120] over GF(2): [1]: [252, 11, 120] Quasicyclic of degree 12 Linear Code over GF(2) QuasiCyclicCode of length 252 with generating polynomials: x^17 + x^16 + x^15 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^2, x^14 + x^12 + x^10 + x^9 + x^8 + x^6 + x^5 + x^4 + x + 1, x^17 + x^15 + x^14 + x^13 + x^10 + x^9 + x^7 + x^6 + x^2 + x, x^17 + x^15 + x^13 + x^12 + x^8 + x^7 + x^5 + x^4 + x^2 + 1, x^14 + x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + 1, x^14 + x^13 + x^12 + x^10 + x^8 + x^7 + x^6 + x^5 + x^3 + x, x^20 + x^19 + x^18 + x^17 + x^16 + x^14 + x^13 + x^12 + x^11 + x^9 + x^8 + x^7 + x^5 + x^2, x^17 + x^15 + x^14 + x^11 + x^10 + x^9 + x^6 + x^5 + x^4 + x, x^17 + x^14 + x^11 + x^10 + x^9 + x^5 + x^4 + x^3 + x + 1, x^17 + x^16 + x^14 + x^12 + x^10 + x^9 + x^7 + x^6 + x^2 + 1, x^11 + x^9 + x^5 + x^3 + x^2 + 1, x^17 + x^16 + x^13 + x^11 + x^10 + x^9 + x^8 + x^4 + x^3 + 1 last modified: 2001-01-30
Lb(252,11) = 120 GB6 Ub(252,11) = 122 follows by a one-step Griesmer bound from: Ub(129,10) = 60 follows by a one-step Griesmer bound from: Ub(68,9) = 30 otherwise adding a parity check bit would contradict: Ub(69,9) = 31 BGV
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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