lower bound: | 52 |
upper bound: | 52 |
Construction of a linear code [76,7,52] over GF(4): [1]: [76, 7, 52] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 1, w^2, 0, 0, 0, w, 0, 1, 0, w, w, w^2, w^2, 1, w^2, 1, w^2, 1, w, w^2, 0, w^2, 1, w^2, w^2, w, 1, 1, 1, w, 0, 0, w, 1, w^2, 0, w, 0, w, 1, 0, w, 1, 1, 0, 0, 1, 0, w, w^2, 1, 1, 1, w, 1, w^2, w, 1, w^2, w^2, 1, w, w^2, w, w, w^2, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 0, w, w^2, 0, 0, w, w, 1, 1, w, 0, 1, 0, w, w, w, w, w, w^2, 1, w^2, w^2, w, w, 0, 1, w^2, 0, 0, w^2, w, 0, w, w^2, w, w^2, w, w, w, w^2, 1, w, w^2, 0, 1, 0, 1, 1, w, 1, w, 0, 0, w^2, w^2, 0, 0, w, 1, w, 0, 1, 0, w^2, w, w^2, 0, w ] [ 0, 0, 1, 0, 0, 0, 0, w^2, w, w, w, w^2, 0, 1, w, 1, 1, 0, w^2, w, w^2, w^2, 0, 1, 0, 1, w^2, 1, 1, 1, 0, 0, 0, 1, w, 0, w^2, 1, w^2, w, 1, 1, 1, w, w, w, w^2, 1, w^2, 0, 1, 0, 0, 1, w^2, 1, 0, 0, w, 1, w^2, 1, 0, w, 0, 0, w, 1, w, 1, 1, w^2, 0, w^2, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w^2, w, w, w, w^2, 0, 1, w, 1, 1, 0, w^2, w, w^2, w^2, 0, 1, 0, 1, w^2, 1, 1, 1, 0, 0, 0, 1, w, 0, w^2, 1, w^2, w, 1, 1, 1, w, w, w, w^2, 1, w^2, 0, 1, 0, 0, 1, w^2, 1, 0, 0, w, 1, w^2, 1, w, w^2, w, 1, 1, w, w^2, w^2, w^2, 1, w, 1, w ] [ 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, w, w, w, 1, 0, 0, w, w^2, w^2, w^2, 0, w^2, 0, w, w^2, 0, w, w, w^2, w, 0, w, w^2, w, 1, 0, w^2, w, w^2, 1, 1, w^2, w, 1, w^2, w, 0, w^2, w^2, w^2, w, 1, 1, 0, 1, 1, 1, w, 1, 1, w^2, w^2, w, 1, 1, 0, 0, 1, w^2, w^2, 1, 0, 0, 1, w^2, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, w, w^2, 0, 0, w, w, 1, 1, w, 0, 1, 0, w, w, w, w, w, w^2, 1, w^2, w^2, w, w, 0, 1, w^2, 0, 0, w^2, w, 0, w, w^2, w, w^2, w, w, w, w^2, 1, w, w^2, 0, 1, 0, 1, 1, w, 1, w, 0, 0, w^2, w^2, 0, 1, 0, 0, 1, 0, w^2, w^2, 1, 0, 1, 0, w^2, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, w^2, 0, 0, 0, w, 0, 1, 0, w, w, w^2, w^2, 1, w^2, 1, w^2, 1, w, w^2, 0, w^2, 1, w^2, w^2, w, 1, 1, 1, w, 0, 0, w, 1, w^2, 0, w, 0, w, 1, 0, w, 1, 1, 0, 0, 1, 0, w, w^2, 1, 1, 1, w, 1, 1, w^2, 0, 0, 1, w^2, 1, w^2, 0, 0, 1, w^2, 1, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-05-17
Lb(76,7) = 51 is found by truncation of: Lb(77,7) = 52 BET Ub(76,7) = 52 follows by a one-step Griesmer bound from: Ub(23,6) = 13 BGV
BGV: Iliya Bouyukliev, Markus Grassl & Zlatko Varbanov, New bounds for n4(k;d) and classification of some optimal codes over GF(4), Discrete Mathematics 281 (2004) 43-66.
Notes
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