lower bound: | 142 |
upper bound: | 142 |
Construction of a linear code [192,5,142] over GF(4): [1]: [194, 5, 144] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, w, 0, w, w, 1, w^2, 0, 0, 1, w, w^2, 0, 0, w, w^2, w^2, w, w^2, 0, w^2, w, 0, w^2, 1, 1, 0, w^2, w^2, 1, w, w, 0, w, 1, w^2, 0, 1, 0, 1, w, 1, w, 0, w, 0, w^2, w, 0, w^2, w, 0, 0, 1, w, 1, 1, w, 1, 1, w^2, 0, w, w^2, w^2, 1, 1, w, 0, 1, 1, w, w^2, w^2, w^2, w^2, 1, 0, 1, 0, w^2, w, 0, w^2, w, w, w^2, 1, w^2, w, w, 1, 0, w, 0, w, 1, w^2, w, 0, w, 1, 1, w^2, w^2, 0, w, 1, 1, w^2, 0, w, w, w, 1, 1, w^2, 0, 0, w, 0, 0, w, w, 1, w^2, 1, w, 0, w^2, w^2, w^2, 0, w^2, w, w, w, 0, 0, w^2, w^2, w^2, 1, w, w^2, 1, w, w^2, 1, 0, w, 1, 1, 0, 0, 0, w, w^2, w^2, 0, w^2, w, 0, w^2, w, 0, 0, w^2, 1, w^2, 1, w, w^2, w, 0, 0, 1, w^2, 0, 0, w, 1, 1, 1, w^2, 0, 0, 1, 1, w^2, 1, w^2 ] [ 0, 1, 0, w, 0, w, w, 1, w^2, 0, 0, 1, 1, 0, w^2, w^2, 1, 0, 0, 1, 0, w^2, 1, 0, w, 1, w^2, w^2, w, 1, 1, w^2, w^2, w^2, 0, w, 1, w^2, 0, 1, 1, 0, w^2, 0, w^2, 1, 0, w, 1, 0, w, 1, 0, w, w, w^2, 1, w, w, 1, w, w, 0, w^2, 1, 0, w^2, 1, 1, w, 0, 1, 1, w, w^2, w^2, w^2, w^2, 1, 0, w, w^2, 0, 1, w^2, 0, 1, 1, 0, w, 1, 0, 0, w^2, w, 0, w, 0, w^2, 1, w^2, 1, w^2, 0, 0, w, w, 1, w^2, 0, 0, w, 1, w^2, w, w, 1, 1, w^2, 0, 0, w, 0, 0, w, w, 1, w^2, 0, w^2, 1, w, w, w, 1, w, w^2, w^2, w^2, 1, 1, w, 1, 1, w^2, 0, 1, w^2, 0, 1, w^2, w, 1, w, w, w^2, w^2, w^2, 1, 0, 0, w^2, w^2, w, 0, w^2, w, 0, w^2, 0, w, 0, w, 1, 0, 1, w^2, w^2, w^2, 1, w, w, 0, w^2, w^2, w^2, 1, w, 1, 0, 0, w, 0, w ] [ 0, 0, 1, 1, 0, 0, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, w, w, w^2, w^2, 0, 0, 1, 1, 0, 0, 0, 0, w^2, w^2, w, w, w, w, 0, 1, 1, 1, w, w^2, w, w, w, 1, 0, w^2, 0, 0, 1, 1, w, w, w^2, w^2, w^2, w^2, w, w, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, w, w, w, 1, 0, 0, 0, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, w^2, w, w, w, 1, 1, 1, 1, 1, w, w, w, w, w^2, w^2, 0, 0, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, 0, 0, w^2, w^2, w, w, 1, 1, 1, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, 0, w^2, w^2, w^2, w, w, w, 1, 1, w, w, 0, 0 ] [ 0, 0, 0, 0, 1, 1, w, w, w, w, w^2, w^2, 0, 0, 0, 0, w^2, w^2, w, w, 1, 1, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, w^2, w^2, 0, 1, 1, 1, w, w^2, w, w, w, 1, 0, w^2, 0, 0, 1, 1, w, w, w^2, w^2, w^2, w^2, w, w, 1, 1, 0, 0, 0, 0, w^2, w^2, 0, 0, 0, 0, 1, 1, w, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, w^2, w, w, w, 1, 1, 1, 0, 0, 0, 1, 1, 1, w, w^2, w^2, w^2, 0, 0, w^2, w^2, w^2, w^2, w, w, w, w, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, w, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, 1, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, w, w, w^2, w^2, w, w, w, w, 1, 1, 1, 1, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 0, w^2, w, w, w, 1, 1, 1, 0, 0, 0, 1, w, w, w, w^2, w^2, w^2, 0, 0, w^2, w^2, 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, 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, 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]: [192, 5, 142] Linear Code over GF(2^2) Puncturing of [1] at { 193 .. 194 } last modified: 2003-01-20
Lb(192,5) = 142 is found by truncation of: Lb(194,5) = 144 BKW Ub(192,5) = 142 is found by considering truncation to: Ub(190,5) = 140 LaM
LaM:
Notes
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