lower bound: | 121 |
upper bound: | 121 |
Construction of a linear code [164,5,121] over GF(4): [1]: [165, 5, 122] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, w^2, 0, 1, 0, w, 0, w^2, 1, w, 0, w, w, w^2, 1, 1, w^2, w, w, 0, w^2, w^2, 1, 1, 0, 1, w^2, 0, 0, 1, w^2, w, 1, w^2, 0, w, 0, w^2, w, 0, 1, w^2, w, 1, w, w, w^2, 1, w, w^2, w, w^2, 1, w^2, 0, w, 0, 1, w, w^2, 1, 1, 0, w, 0, w, 1, 1, 0, w, w^2, w, 0, 0, 1, w^2, 1, w^2, 1, w^2, w, 0, w^2, 1, 0, w, 0, w^2, 0, w, w, 1, 0, 1, w^2, w, w^2, 0, w, 0, w^2, w^2, 0, w, w, w^2, 1, 1, 1, w^2, w, 0, w, 1, w^2, 0, 1, w, 0, w^2, 1, 0, 0, w, w^2, 1, w^2, 1, 0, w^2, 1, w, 0, 1, w^2, 0, w, 0, 1, w^2, w, 1, 1, w, w^2, 1, 1, 0, w, w^2, w, 0, w, 0, 1, w^2, w, 0, 0, w, w^2, 1 ] [ 0, 1, 0, 0, 0, w^2, w^2, w, 1, w^2, w^2, 1, w, 1, w^2, w, w, 0, w^2, 0, 1, 0, w, 1, w, 0, 1, 0, w, 0, w, w^2, w, 0, w, 1, w, 1, w^2, 1, 1, 0, w^2, w^2, 1, 0, 0, w^2, w, w^2, 1, w^2, w, 0, 1, w, 0, w^2, 0, w, w^2, w^2, w, 0, 1, 0, w, 1, w^2, 0, 1, 0, w, 0, 1, w^2, w, w^2, 1, w^2, 1, w, 0, 1, w^2, w^2, 1, 0, w, 1, w, w^2, 1, 0, w^2, 1, 0, w, w, w^2, 0, w^2, 1, 1, 0, w^2, 1, 0, 1, w^2, w, 1, w^2, w, 0, w^2, 0, w, 1, 1, w, 0, 0, w, w^2, w, 0, 1, w^2, 1, w^2, w^2, 0, 1, w^2, 1, 0, w, 1, w, 0, 1, w^2, 1, w, w^2, 0, 0, w, w^2, w, 0, w, w^2, 1, w, 0, 1, w, w^2, w, w^2, 1, w, w ] [ 0, 0, 1, 0, w^2, w^2, w, w^2, w, w, 1, 1, 1, 0, 0, w, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w^2, 0, w^2, w^2, w, w, w, w, 1, 1, 0, 0, 0, w^2, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, w^2, 1, 1, w, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, w, w, w, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w^2, w^2, w, w, 1, 1, 1, 0, 1, 1, 0, 0, w^2, w, w, w, 0, 0, 0, 1, w, w, w, w, w^2, w^2, w^2, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, 1, 1, 0, 0, 0, w^2, w^2, w^2, w, w, w, w, w, 1, 0, 0, w^2, 0 ] [ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [164, 5, 121] Linear Code over GF(2^2) Puncturing of [1] at { 165 } last modified: 2002-03-26
Lb(164,5) = 120 is found by truncation of: Lb(172,5) = 128 Liz Ub(164,5) = 121 follows by a one-step Griesmer bound from: Ub(42,4) = 30 follows by a one-step Griesmer bound from: Ub(11,3) = 7 is found by considering truncation to: Ub(10,3) = 6 GH
Liz: P. Lizak, Optimal quaternary linear codes, Ph. D. Thesis, Univ. of Salford, Nov. 1995.
Notes
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