lower bound: | 89 |
upper bound: | 98 |
Construction of a linear code [216,18,89] over GF(2): [1]: [219, 18, 92] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 219 with generating polynomials: x^72 + x^70 + x^66 + x^64 + x^61 + x^59 + x^58 + x^57 + x^54 + x^47 + x^43 + x^42 + x^41 + x^34 + x^33 + x^31 + x^29 + x^25 + x^22 + x^21 + x^20 + x^19 + x^18 + 1, x^72 + x^68 + x^66 + x^65 + x^64 + x^59 + x^58 + x^57 + x^56 + x^55 + x^53 + x^51 + x^49 + x^46 + x^44 + x^39 + x^36 + x^35 + x^32 + x^31 + x^30 + x^29 + x^24 + x^23 + x^21 + x^20 + x^19 + x^18 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^3, x^72 + x^71 + x^70 + x^65 + x^64 + x^61 + x^60 + x^58 + x^53 + x^51 + x^50 + x^47 + x^45 + x^44 + x^42 + x^41 + x^37 + x^36 + x^35 + x^32 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^21 + x^20 + x^18 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^4 [2]: [216, 18, 89] Linear Code over GF(2) Puncturing of [1] at { 217 .. 219 } last modified: 2016-11-16
Lb(216,18) = 88 is found by shortening of: Lb(217,19) = 88 GW2 Ub(216,18) = 98 is found by considering shortening to: Ub(215,17) = 98 otherwise adding a parity check bit would contradict: Ub(216,17) = 99 BK
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
|