lower bound: | 46 |
upper bound: | 48 |
Construction of a linear code [110,14,46] over GF(2): [1]: [112, 14, 48] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 112 stacked to height 2 with generating polynomials: x^10 + x^8 + x^6 + 1, x^12 + x^11 + x^9 + x^8 + x^7 + x^6 + x^4 + x, x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x + 1, x^13 + x^12 + x^11 + x^8 + x^6 + x^5 + x^4 + x, x^9 + x^8 + x^5 + x^4 + x^3 + x^2 + x + 1, x^13 + x^12 + x^10 + x^7 + x^4 + x^3 + x + 1, x^8 + x^4 + x^2 + 1, x^12 + x^11 + x^10 + x^7 + x^5 + x^4 + x^3 + 1, x^12 + x^10 + x^6, x^9 + x^7 + x^3, x^10 + x^7 + x^6 + x^5 + x^4 + x^2 + x, x^13 + x^11 + x^10 + x^9 + x^3 + x^2 + 1, x^10 + x^9 + x^5 + x^3 + x^2 + x + 1, x^13 + x^11 + x^10 + x^8 + x^7 + x^6 + 1, x^13 + x^11 + x^9 + x^7 + x^5 + x^3 + x, x^10 + x^9 + x^5 + x^3 + x^2 + x + 1 [2]: [110, 14, 46] Linear Code over GF(2) Puncturing of [1] at { 111 .. 112 } last modified: 2010-11-13
Lb(110,14) = 44 is found by taking a subcode of: Lb(110,15) = 44 is found by lengthening of: Lb(107,15) = 44 is found by adding a parity check bit to: Lb(106,15) = 43 is found by construction A: taking the residue of: Lb(191,16) = 85 is found by truncation of: Lb(192,16) = 86 BZ Ub(110,14) = 48 follows by a one-step Griesmer bound from: Ub(61,13) = 24 follows by a one-step Griesmer bound from: Ub(36,12) = 12 is found by considering shortening to: Ub(33,9) = 12 He
He: P.W. Heijnen, Er bestaat geen binaire [33,9,13] code, Afstudeerverslag, T.U. Delft, Oct. 1993.
Notes
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