lower bound: | 166 |
upper bound: | 168 |
Construction of a linear code [228,6,166] over GF(4): [1]: [230, 6, 168] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, w^2, 1, w, 0, 1, 1, w, 1, w, w, 0, w, 1, 1, w^2, 0, w, 1, 0, w, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, 0, 0, 1, w, 0, 0, 1, w^2, 0, 0, 0, w, 0, w, 0, w, w^2, w^2, w^2, w^2, w, 1, 1, w, w^2, 0, w, w^2, 1, 0, 0, 1, 1, 0, w^2, w^2, w, 0, w^2, w, w^2, 1, w, w, w, 1, 0, w^2, 0, w^2, w^2, 0, w, 0, 0, w, w, w, w, w, 0, 1, 0, 0, w, 0, 1, 1, 0, w^2, 1, w^2, w^2, w, w, 1, 0, w, w^2, 1, 1, 0, 0, w^2, w, 1, 1, w^2, w^2, w, w^2, w^2, 0, w^2, w, w, w^2, 1, 0, 1, w, 0, 0, w^2, 0, w^2, w, 1, 1, w^2, w^2, w^2, w, w^2, 1, w^2, 0, 1, 1, w, w^2, 0, 0, w, w, w^2, w^2, w, w, w^2, w^2, 1, w, 1, w, 0, w^2, 0, 0, w, w, w^2, w^2, 1, 0, 0, w, w, 0, 0, 1, 1, w, w, w^2, w^2, w^2, w^2, 0, w^2, w, 1, 1, 1, 1, w, 1, 1, w, 1, w, 0, w^2, 1, 1, 1, w, w^2, 0, 1, 0, w^2, w, 1, 1, w, 1, 0, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, w, w, 0, w, 0, 1, w, w^2, 0, 0, 1, 0, w, 1, w^2, w^2, 1, 1, 0, w^2, w^2, 1, w, w^2, 0, 0, w^2, w, 1, 0, w^2, w, w, 1, 0, w^2, w^2, 0, 1, 1, w, w^2, w^2, w^2, 0, 1, 0, 0, 0, 0, w, w, 0, w, w, w^2, w, 1, 0, w, w^2, w, w, 1, w^2, w^2, w^2, 1, 0, 1, w, 0, 0, 1, w, w^2, 0, w, 1, 0, 0, 1, w^2, 0, w, w, w^2, 1, 1, 1, 1, 0, w^2, 0, w^2, w^2, 1, w^2, w^2, w, w, 1, 1, w^2, 1, w^2, 1, w^2, 0, 1, w, w, w^2, w, 0, w, 1, 1, w, 0, w^2, w^2, 1, 0, w, w, w^2, 1, 0, w^2, 1, 1, w^2, 1, 0, w, 1, w^2, 0, w, 1, w^2, w, 0, 1, 1, w, 0, w, 1, 0, w^2, 1, w^2, 0, w, w^2, 1, 0, w, w, 1, w, 0, 0, w^2, 0, 0, w^2, w^2, 0, 0, 1, 1, w^2, 0, 0, w^2, 1, w^2, w, w^2, w^2, 1, 0, w, 1, w^2, w^2, w^2, 0, 0, w, w, w^2, w^2, 0, w, 1, w, w, w, w^2, 1, 0, w, w, w, w, 1, 1, w, w^2, 0, w^2, 0, w, 1, w^2 ] [ 0, 0, 1, 0, 0, 0, w^2, w, 0, w^2, 1, w^2, w^2, w^2, w^2, 0, 0, w^2, w^2, w^2, w^2, w^2, 0, w^2, w^2, w, 1, w^2, 0, 1, w^2, w, w^2, 1, 0, w^2, 0, w^2, 0, 0, w^2, 0, 1, 0, 1, w, w, 1, 0, w, 1, w^2, 0, 0, w, 0, w, w, w, w, w, 1, w, 0, w, w^2, 1, w^2, w, w, w, w, 1, w^2, 1, w^2, w^2, 0, 0, 1, 1, w^2, 0, w, 0, 1, w^2, w, w, 1, w^2, w^2, 1, 0, 1, 0, w, 1, w^2, 0, 0, w^2, 0, 1, w, w^2, w^2, 0, w, 1, w^2, w, w, 1, w, w, w^2, 0, 0, 1, w^2, 0, w, w, w, w, 1, w, 0, 0, w^2, 0, 0, w, 0, 0, w^2, w^2, w^2, w^2, w, w, w, 0, 1, w, w^2, 1, 0, 1, 0, w^2, w, w, w^2, 0, w^2, w^2, w^2, 1, 1, 1, 1, w, 1, 1, 1, 0, w, w, 1, w, w^2, w^2, w^2, 0, w, 1, 0, w^2, 1, 0, w, w^2, 0, w^2, 1, w^2, w^2, w^2, 0, 0, w, 1, w^2, w^2, 1, w, 0, 0, 1, w^2, 0, w, 1, 0, w^2, w, 0, 0, w^2, w, 0, 1, 0, 0, w, w, w, w, 1, w^2, 0, 1, w, 0, w, w, w, w ] [ 0, 0, 0, 1, 0, 0, 1, w^2, 0, w, w^2, w^2, w^2, w^2, w^2, 0, w^2, w^2, 0, 0, 0, 0, 0, 0, w^2, 1, w^2, 0, w^2, w, w^2, w^2, 0, 1, 1, w, w, w^2, w, 0, 0, w, 0, w, 1, 1, w^2, 0, w^2, w^2, 1, 1, 1, 1, 1, 1, w, w, 1, 0, w^2, w, w, 0, 0, 0, 1, w^2, w, w^2, 0, 1, w^2, 1, w, w^2, 1, 0, w^2, 1, w^2, 1, w, w^2, 1, w^2, w, w, 0, 1, w^2, w, w^2, w, w, w^2, w^2, w^2, 1, w, 0, 0, w, w^2, 1, 1, 0, w, w, w, w, 1, 0, 1, 0, w^2, 1, 1, 0, w, 1, w, w^2, w^2, w, 0, 1, 1, w, 1, w, w^2, 0, 0, w^2, 1, 1, w, w^2, 0, w, 0, 1, w, w^2, w^2, w, 0, 1, w, 0, w, 1, w, w, 1, 1, 0, 1, 1, w, w^2, 0, w, 0, w^2, w, w^2, w, w, w^2, w^2, 0, w^2, 0, 1, w, w^2, 1, w, 1, 0, w, w^2, w, w, 1, 0, 0, w, w^2, w^2, 0, w, 0, w^2, w, 0, 1, 0, 0, w^2, 1, w^2, 0, w, 0, 0, 1, 1, w, 0, 0, 0, 0, w, w, w^2, 1, 0, 0, w, w, w, w, 0, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 1, 0, w, 1, w^2, w, 1, w, w, w, w, w, 1, w, w, w, w, w, 1, w, 1, w^2, w, w, w, w, 1, 1, w^2, 0, 1, 1, w, 0, w, w^2, 0, 1, w, 1, w^2, 0, w, w^2, 1, w^2, w, w^2, 0, 0, w, 1, 0, 0, w^2, w, 1, w, 1, 1, w^2, w, 1, 1, 1, 1, w, w^2, w, 1, 0, w^2, 1, w, 1, w, 0, w^2, w^2, 0, 0, w^2, 0, 1, w^2, 1, 1, 1, w, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, 1, 0, 1, 0, 1, 0, w, w, 0, w, w^2, 1, w^2, 1, w, 1, 1, w, w^2, w^2, 0, 1, w^2, 0, 1, w, w^2, 0, 0, w, 1, w^2, w, 0, w, w, w, w, 0, w^2, w, w, w, 1, 1, 1, 1, 0, w^2, w^2, 1, 1, 0, 1, w, w, w^2, 1, w, w^2, 0, 1, 0, w, w^2, w^2, 0, w^2, 1, w, 0, w^2, 0, w, w^2, 0, w^2, w^2, w, 1, 1, 1, w^2, 1, 0, w, w, 0, w, w^2, w, w^2, w^2, w^2, 0, 1, w, w^2, w, w^2, w, w^2, w^2, 0, 1, 0, w^2, w^2, w^2, w^2, 1, 0, 1, w, w, w^2, 1, 0, 0, 1, 1, 1, 1, 1, w^2, 0, 1, w ] [ 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [228, 6, 166] Linear Code over GF(2^2) Puncturing of [1] at { 229 .. 230 } last modified: 2006-09-17
Lb(228,6) = 166 is found by truncation of: Lb(230,6) = 168 Koh Ub(228,6) = 168 follows by a one-step Griesmer bound from: Ub(59,5) = 42 is found by considering shortening to: Ub(58,4) = 42 is found by considering truncation to: Ub(56,4) = 40 HLa
Koh: Axel Kohnert, email, 2006.
Notes
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