lower bound: | 109 |
upper bound: | 110 |
Construction of a linear code [224,9,109] over GF(2): [1]: [225, 9, 110] Quasicyclic of degree 25 Linear Code over GF(2) QuasiCyclicCode of length 225 with generating polynomials: x^2 + x, x^8 + x^7 + x^4 + x, x^7 + x^6 + x^5 + x^3 + x^2 + 1, x^8 + x^7 + x^6 + x + 1, x^3 + x, x^7 + x^6 + x^4 + x^3 + x^2 + x + 1, x^7 + x^6 + x^5 + x^2 + x, x^4 + x^3 + x^2 + x, x^8 + x^7 + x^5, x^8 + x^6 + x^3 + x + 1, x^8 + x^7 + x^6 + x^5 + x^3 + x^2 + x, x^8 + x^7 + x^6 + x^3 + x^2 + x + 1, x^7 + x^4 + 1, x^6 + x^5 + x, x^5 + x^2 + x + 1, x^8 + x^7 + x^6 + x^5 + x^3 + 1, x^8 + x^7 + x^5 + x^3 + x^2, x^7 + x^5 + x + 1, x^5, x^8 + x^5 + x^3, x^8 + x^6 + x^5 + x^3 + x, x^7 + x^6 + x^5 + x^4 + x^3 + 1, x^8 + x^3 + 1, x^6 + x^4 + x^2 + x + 1, x^6 + x^5 + x^4 + x^2 + x [2]: [224, 9, 109] Linear Code over GF(2) Puncturing of [1] at { 225 } last modified: 2001-04-27
Lb(224,9) = 109 is found by truncation of: Lb(225,9) = 110 Gu9 Ub(224,9) = 110 follows by a one-step Griesmer bound from: Ub(113,8) = 54 follows by a one-step Griesmer bound from: Ub(58,7) = 27 vT3
vT3: H.C.A. van Tilborg, The smallest length of binary 7-dimensional linear codes with prescribed minimum distance, Discr. Math. 33 (1981) 197-207.
Notes
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