lower bound: | 103 |
upper bound: | 107 |
Construction of a linear code [148,7,103] over GF(4): [1]: [149, 7, 104] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w, 0, 1, w, w^2, 0, w^2, 1, 1, w, 0, w^2, w, w, 1, w, w^2, 0, 0, w, 1, 0, 1, w, w^2, w, w^2, 1, 0, 0, w, w^2, 1, 1, w, 1, 1, w^2, 0, w^2, 1, 0, w, 1, 1, 1, 0, w^2, w^2, 1, w, w, w, w^2, 0, 0, 1, 0, w^2, w, 1, 0, 1, w, w, w^2, w^2, w, 1, w, w, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, w^2, w^2, 1, 1, 1, 1, w^2, w, 1, w, 0, w, 1, w^2, 1, 1, w, 0, 1, 1, 1, 1, w^2, w^2, w^2, 0, 0, w^2, 0, w^2, w, w, 0, w^2, 0, 0, 1, w, 0, 1, w, 1, w, 0, w^2, w^2, 0, 0, 1, 1, 1, w^2, 0, 0, w, w, 1, 0, 0, w ] [ 0, 1, 0, 0, 1, 0, 0, 0, 1, w^2, 0, 1, w, w, 0, w^2, 0, w, 1, 0, 0, 1, w^2, w, w, 0, w^2, w, 1, 1, w, w, 1, 1, w, 1, 0, w^2, w^2, w, 0, w^2, 1, w, 0, 0, 1, 1, 0, 0, w, 1, w, 1, 1, 1, w^2, w^2, w^2, w^2, 0, w^2, 0, 1, w^2, w^2, 1, 0, 1, w, 1, 0, 0, w, 1, 1, 0, 1, 1, w, 1, 1, 0, 0, 1, 1, 0, w^2, 0, 0, 0, 0, w^2, w, 0, 1, w^2, w, w^2, 0, 1, 0, w^2, w, w^2, w, w^2, 0, 1, w^2, w^2, w^2, 0, 0, 1, w, 0, w, w^2, w^2, 1, 0, w, 1, 1, w^2, 1, 0, 1, w^2, 0, 1, w, 1, w, w^2, 1, w, w, 0, 0, 0, w^2, w, 1, w, 1, 0, w^2 ] [ 0, 0, 1, 0, 1, 0, 0, 0, 0, w, w^2, 1, w^2, 1, w, 1, 0, 1, w, 0, w, w^2, w, w^2, 0, w^2, 1, w^2, w, 1, w, w^2, w, w^2, w^2, 0, w^2, 0, w^2, 1, w, w, 1, 0, w, 1, 1, 1, 0, w, w^2, w, w, 0, w, w, 1, w, w, 1, w^2, 0, w^2, 0, 0, w, w^2, w^2, 0, w, 0, w, w, w, 0, w^2, 1, w, 0, 0, 0, 1, 1, 0, 1, 0, 0, w, 1, w^2, 1, w^2, w, w, w, 1, 0, 1, 0, w, 0, 0, 0, 1, w^2, w, w^2, 1, w, 1, 0, 0, 1, w, w^2, 0, w, w, 0, 0, w^2, 1, w^2, w, w, 1, 0, 0, 1, 1, w, w^2, 1, w^2, w^2, w^2, 1, 0, 0, 0, 1, w^2, w, w, w^2, w, w^2, 1, 0 ] [ 0, 0, 0, 1, 1, 0, w, 0, 0, 0, w, 1, w, w, w^2, 0, 0, w^2, 0, 1, 1, w, 1, 0, w, 0, 1, 1, w^2, w, w, 0, w^2, w^2, w, w^2, w^2, w, w, w, 0, w, 0, w^2, 0, w^2, w, w, 0, 1, w, w^2, 1, w^2, 0, w, 0, w^2, 1, w^2, 1, 0, 1, 0, 0, w^2, w^2, w, w, 1, w, w^2, 0, 1, 0, 1, 1, 1, 1, w, 1, 0, 0, 0, 0, 0, 1, w^2, w^2, 0, w, w, 0, 0, w, w^2, 1, w, w^2, 0, w, w, 1, w^2, w, 0, 1, 0, 0, 1, w, w^2, 1, w^2, w^2, w, 0, 1, w, 0, w^2, w, 1, w^2, w, 0, 1, 0, 1, w, 1, 1, w, 0, w^2, 0, 0, w^2, 1, w^2, 0, 1, w, w^2, 1, 1, 0, w^2, 1 ] [ 0, 0, 0, 0, 0, 1, 1, 0, 0, w^2, w^2, w^2, w, w, 1, 1, 0, w, w^2, 1, w, w, 1, 0, w^2, 0, w, w^2, 0, w^2, 0, w^2, 0, w^2, w, w^2, 1, 1, 0, 0, 0, 0, w^2, 0, 0, w^2, w, w, w, w, w^2, w, 1, 1, 0, w, 0, 1, w^2, w^2, w^2, 0, w^2, w, w, w, w, 0, 1, w^2, 1, 0, 1, 0, 1, w, w^2, w^2, 0, 1, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, 1, w^2, w^2, 0, 0, 0, w, w, 0, 1, 0, 0, 1, w, 0, w^2, 1, 1, w^2, 1, 1, w, 1, w^2, w, w, w^2, w, 0, w^2, w^2, 0, 1, w^2, 0, w, w^2, w^2, 0, 1, w^2, w, w^2, 1, w, 1, 1, w^2, 1, 1, w, 0, 0, w^2, w, w, w^2 ] [ 0, 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, 0, 1, 1, 1, 1, 1, 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, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 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, 1, w^2, w, 1, 1, 1, w, w^2, 1, 1, w^2, w, 1, w, 1, w^2, 1, w, w, w^2, w, w, w^2, w, w, 1, w, 1, 1, w, w^2, w^2, w^2, w^2, w, w, 1, 1, w^2, 1, w^2, w, 1, 1, 1, 1, w, w, w^2, w^2, w^2, 1, 1, w^2, w, w^2, w, w, w^2, w^2, w, w, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w, 1, 1, 1, w, w, w^2, w, w^2, w, w^2, w^2, 1, w, 0, 0, 0, 0, 0, w, 1, w, w^2, w^2, w^2, 1, w^2, 1, 1, w, w^2, 1, 1, w^2, w^2, w, 1, 1, w^2, w, w^2, w, 1, w, w^2, 1, w^2, w^2, w^2, 0, 0, 0, 0, 0, w ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [148, 7, 103] Linear Code over GF(2^2) Puncturing of [1] at { 149 } last modified: 2008-08-11
Lb(148,7) = 102 is found by truncation of: Lb(151,7) = 105 Koh Ub(148,7) = 107 is found by considering truncation to: Ub(144,7) = 103 DM3
Koh: Axel Kohnert, email, 2006.
Notes
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