lower bound: | 74 |
upper bound: | 82 |
Construction of a linear code [184,18,74] over GF(2): [1]: [186, 18, 76] Quasicyclic of degree 2 Linear Code over GF(2) QuasiCyclicCode of length 186 with generating polynomials: x^92 + x^86 + x^85 + x^84 + x^82 + x^81 + x^80 + x^77 + x^75 + x^74 + x^71 + x^70 + x^69 + x^68 + x^66 + x^64 + x^62 + x^58 + x^56 + x^55 + x^54 + x^52 + x^50 + x^48 + x^46 + x^45 + x^40 + x^39 + x^38 + x^36 + x^35 + x^31 + x^28 + x^26 + x^23 + x^22 + x^20 + x^18 + 1, x^90 + x^87 + x^84 + x^82 + x^80 + x^78 + x^76 + x^74 + x^72 + x^69 + x^68 + x^67 + x^66 + x^64 + x^63 + x^61 + x^59 + x^58 + x^56 + x^55 + x^48 + x^46 + x^45 + x^43 + x^40 + x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^27 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^16 + x^14 + x^6 + x^2 + 1 [2]: [184, 18, 74] Linear Code over GF(2) Puncturing of [1] at { 185 .. 186 } last modified: 2004-11-02
Lb(184,18) = 73 is found by truncation of: Lb(189,18) = 78 is found by adding a parity check bit to: Lb(188,18) = 77 GW2 Ub(184,18) = 82 is found by considering shortening to: Ub(182,16) = 82 otherwise adding a parity check bit would contradict: Ub(183,16) = 83 BK
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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