lower bound: | 40 |
upper bound: | 42 |
Construction of a linear code [96,12,40] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [92, 11, 40] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 92 with generating polynomials: x^22 + x^20 + x^18 + x^16 + x^15 + x^14 + x^11 + x^5, x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^14 + x^12 + x^11 + x^6 + x^5 + 1, x^19 + x^16 + x^14 + x^11 + x^9 + x^5 + x^3 + x, x^21 + x^20 + x^18 + x^17 + x^12 + x^10 + x^9 + x^8 + x^4 + x^2 + x + 1 [3]: [92, 13, 38] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 92 stacked to height 2 with generating polynomials: x^22 + x^18 + x^17 + x^16 + x^14 + x^12 + 1, x^22 + x^19 + x^16 + x^15 + x^14 + x^13 + x^12 + x, x^22 + x^19 + x^18 + x^16 + x^15 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^2 + x, x^18 + x^14 + x^12 + x^9 + x^8 + x^7 + x^4 + 1, x^22 + x^19 + x^16 + x^15 + x^14 + x^13 + x^12 + x, x^21 + x^18 + x^16 + x^15 + x^14 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3, x^21 + x^19 + x^16 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^4 + x^2, x^19 + x^18 + x^15 + x^14 + x^13 + x^12 + x^10 + x^7 + x^5 + x^4 + x + 1 [4]: [95, 13, 40] Linear Code over GF(2) ConstructionX using [3] [2] and [1] [5]: [96, 13, 40] Linear Code over GF(2) ExtendCode [4] by 1 [6]: [96, 12, 40] Linear Code over GF(2) Subcode of [5] last modified: 2001-01-30
Lb(96,12) = 40 is found by taking a subcode of: Lb(96,13) = 40 is found by lengthening of: Lb(95,13) = 40 CZ Ub(96,12) = 42 is found by considering shortening to: Ub(95,11) = 42 otherwise adding a parity check bit would contradict: Ub(96,11) = 43 Bro
CZ: Chen Zhi, Six new binary quasi-cyclic codes, IEEE Trans. Inf. Theory 40 (1994) 1666-1667.
Notes
|