lower bound: | 67 |
upper bound: | 68 |
Construction of a linear code [96,6,67] over GF(4): [1]: [97, 6, 68] Linear Code over GF(2^2) code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, w, 0, 0, 0, 1, 0, w, 0, 1, w^2, 0, 0, w^2, w^2, w, 1, 1, 0, w^2, w^2, w^2, 1, w^2, 0, 0, 0, w^2, 1, 0, w^2, 0, w^2, w^2, 1, 0, w^2, 1, w, 1, w^2, w, 1, 0, w, w^2, w, 0, 1, 1, w, w, w^2, w^2, w^2, 1, 0, 1, 1, 0, 1, 0, w^2, w, 1, 1, 0, w^2, w^2, w, w, w^2, 1, 1, w^2, w^2, w, w^2, 1, 1, w^2, 1, 1, 1, w^2, 1, w, w^2, 1, 0, 1, 0, w^2, w^2 ] [ 0, 1, 0, 0, w^2, 0, 0, 0, w^2, w^2, 1, 0, w^2, w^2, w^2, 0, w, 1, 1, 0, w^2, w^2, 0, w^2, 0, 1, w^2, 1, 0, w, 0, 1, w^2, 1, w, w, w^2, w, w^2, 1, 0, w, 0, w, 1, 0, 1, 0, w^2, 1, 1, 1, 0, 1, 1, w^2, 1, 1, w, 1, 0, 0, w^2, w^2, w^2, w^2, w, w, 1, 0, w, 0, w^2, w, 0, 1, w, w^2, 0, 0, 1, 0, 1, 1, w, w, 0, 1, w, w, w, 0, 0, 1, w^2, 1, 1 ] [ 0, 0, 1, 0, w^2, 0, 0, 0, 1, w, 1, 0, 0, 0, w^2, w, 1, 0, w, 0, 1, 1, w, w^2, 0, 0, 0, 1, w^2, w, w^2, w, 1, 0, 0, 1, w, w^2, w, 1, w^2, w, w, 0, 1, w^2, w, w^2, w^2, 1, 0, w^2, 1, 0, w^2, 1, 1, w, 0, w^2, 1, 0, w^2, w, 1, w, w, 0, 0, 1, w^2, w, 1, w^2, 1, w, 1, w, 1, w^2, w, 1, w, w^2, 1, w^2, 1, w^2, 1, 1, w^2, 0, w, 0, w^2, w^2, w^2 ] [ 0, 0, 0, 1, 1, 0, 0, w^2, w^2, w, w^2, 1, 1, w^2, w^2, 1, w^2, 0, w^2, w, w, 1, w^2, 0, w^2, 1, 0, w^2, w^2, 1, 0, 0, 1, w^2, w^2, 0, 0, 0, 1, 1, 0, w, 0, 0, 0, 0, 0, w^2, w, 1, w, 0, 0, w, w, w, 1, w, w, 0, w, w^2, w, w^2, w, 0, 1, w, 0, 0, w^2, 1, 1, w^2, w, w, 1, w, 0, w, 0, 1, 1, w, 1, 1, w, 1, w, 1, 0, w, w, w^2, 0, w, w ] [ 0, 0, 0, 0, 0, 1, 0, w^2, w, 0, 0, w, 0, w, w, w^2, 0, 1, 1, w, 0, 0, w, w^2, 0, w, 1, w, 1, 0, w, w, w, w^2, 1, 0, w, w, w^2, w, 1, 0, 0, w^2, 1, w^2, w, 0, w, 1, w^2, 1, w, 1, w, 1, 0, 0, 1, w^2, w, w, w^2, w^2, 1, 0, 1, 0, 1, w, 1, 0, 1, w^2, w, 1, w^2, w, 1, 1, w^2, w^2, 1, w^2, 1, w^2, 1, 1, w^2, w^2, 0, w^2, w, 0, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [96, 6, 67] Linear Code over GF(2^2) Puncturing of [1] at { 97 } last modified: 2006-03-27
Lb(96,6) = 67 is found by truncation of: Lb(97,6) = 68 Koh Ub(96,6) = 68 follows by a one-step Griesmer bound from: Ub(27,5) = 17 is found by considering truncation to: Ub(26,5) = 16 BGV
Koh: Axel Kohnert, email, 2006.
Notes
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