lower bound: | 148 |
upper bound: | 150 |
Construction of a linear code [204,6,148] over GF(4): [1]: [203, 6, 148] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, w^2, w, 1, 0, 0, 1, 0, 1, 1, 1, w, 0, w, w^2, w^2, w, w, 1, w^2, w^2, 1, w^2, 1, w, 1, w^2, 1, w, w^2, w^2, w^2, 1, w^2, 0, 1, w, w, w^2, 0, 1, 1, 1, 0, 0, 0, w^2, w^2, 0, 0, w^2, w^2, 1, w^2, 0, w^2, w, 0, w, w, w^2, w, w^2, 1, 1, 0, w^2, 0, 0, w, w, 1, w^2, w, 0, w^2, 0, w^2, 0, 0, 0, 1, w^2, 1, w^2, w, w, 1, w, 0, 0, w, w, w, 1, 1, 0, 1, w, 1, 1, w, w^2, 0, 0, w^2, 1, w, w, w, 1, 1, 0, w^2, 1, w^2, 1, 1, w^2, 1, w^2, w, 0, w, 1, w^2, 1, w^2, 1, 0, 0, w^2, w^2, w^2, 0, w^2, w^2, 0, 1, w^2, 0, 0, w, 0, w^2, 0, 1, w^2, 1, 1, 0, 1, 0, w, 1, 1, 0, 0, 1, 0, w, 0, w, 1, w, 0, w, 0, 0, w, w^2, 0, w^2, w^2, 1, 1, w, 0, 1, w^2, 0, w^2, 0, w^2, w^2, 0, w^2, 1, w^2, 0, 1, 1, w^2, 0, 0, 1, w, 1, w, 0, w^2, w ] [ 0, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w, w, 0, w^2, w, 0, w^2, w, w^2, 0, w, w^2, 1, 0, w, w^2, w^2, w, 0, 0, w^2, w, 1, 1, 1, 0, w, 1, 0, w^2, w^2, 1, 1, w^2, 0, 0, w, 0, 1, 0, w, 1, 0, w^2, w^2, w, 0, 0, 1, 0, w, 0, w^2, w, 0, w, 1, 0, 0, 1, 1, w, 1, w, w^2, w^2, w, 1, w^2, 1, w^2, w^2, w^2, w, 1, w, 1, w, w^2, w^2, w, w^2, w^2, 1, 1, 1, 0, w, w, w^2, 0, w, w, w, 0, 1, w^2, w, w^2, 0, 0, w, 1, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w, 0, 1, 0, w, 1, 1, 0, w, w, w^2, w, 1, w, 1, w^2, w^2, w, w, 1, 0, w^2, w^2, w, 0, 0, 1, 0, w, 0, w^2, w, 0, w, 1, 0, w, 0, w^2, w^2, w, 0, 1, 0, w^2, 0, 0, w, w, 1, 0, 0, 1, 1, w, 1, w, w^2, w^2, w, 1, w^2, 1, w^2, w^2, w, w^2, 1, w, 0, w^2, w, w^2, 0, 1, 1, 1, 0, w, w^2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 0, w^2, w^2, w, w, 0, w, 0, w, w^2, 1, w, 0, w^2, w^2, w^2, 0, w^2, w, 1, w^2, 0, w^2, w^2, w, w, 0, 0, w, 1, 1, 1, w, w^2, 0, w^2, 0, 1, w, 0, w^2, w, 1, 1, 1, 0, w, 0, w, w^2, 0, 0, w^2, w, w, w^2, w^2, 1, w, w^2, w^2, w^2, w, 0, 1, 0, 1, w^2, w, 1, 0, w, 1, w^2, 0, w^2, w, 0, 0, 0, 1, w, 1, 1, w^2, w^2, w, 0, w^2, w, 1, 0, 0, w^2, 1, w, w^2, w^2, 1, w, 0, w, w, w^2, 1, 0, w, w, w^2, 0, 1, w^2, w^2, 0, 1, w, 1, w, 1, 0, w, 1, w^2, w, 1, 1, 0, w^2, 0, w^2, 0, w, w^2, w^2, w^2, w, 0, w, 0, 1, w, w, 1, 0, 0, 1, 1, w^2, w, 0, w^2, w, 1, w^2, w, w, 0, 1, 0, 1, 0, w^2, w^2, 0, 1, 1, 1, 0, w, w^2, w, w^2, 1, 0, w^2, w, 0, w^2, 1, w, 1, w^2, w, 0, w, 0, w, w, w^2, w^2, 0, w^2, 0, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, w, w, 0, w^2, w^2, w, 1, w^2, 0, w, w, w, 1, w^2, 0, 1, 1, 0, 1, 1, 0, w, w, 0, w, w, 0, w, 1, 0, w, w^2, 0, w, w, 1, w^2, 1, w^2, 1, 0, 1, w^2, 0, w, 1, 1, w^2, w, 0, w^2, w^2, w, 0, 1, 0, 0, w^2, w, 0, w^2, 1, 0, w^2, w^2, w, 1, w, 1, w, 0, 1, w, w^2, w^2, w^2, w, 0, 1, 0, 1, w^2, w, 1, 0, w, 1, w^2, 0, w^2, w, 0, 0, 0, 1, w, 1, 1, w^2, w^2, w, 0, w^2, w, w^2, 1, w, w, w, 0, 1, 0, 0, w^2, w^2, 1, w^2, w^2, w^2, w, 0, w, 0, 1, w, w, 1, 0, 0, 1, 1, 0, w, 1, w^2, 0, 0, w, w^2, 1, w, w, w^2, 1, 0, 1, w, w, w, 0, w^2, 0, w^2, 1, 0, 0, 1, w^2, w^2, 1, 1, 1, w, w^2, 1, w, 0, 1, w, w, w^2, 0, w^2, 0, w^2, 1, w^2, w, 0, 1, 1, w, 1, w^2, 0, 1, 1, 0, w^2, w^2, 0, 1, 1, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w, w^2, w^2, 1, w, w^2, 1, w, w^2, w, 1, w, w^2, 1, 1, w^2, w, w, w^2, 1, 1, w, w^2, 0, 0, 0, 0, w, 1, w^2, 0, 0, w, w^2, 1, w, w, w^2, 1, 0, 1, w, 1, 0, 0, 0, 1, w^2, w, w^2, w, 0, 1, w, w^2, 1, w, 1, 0, w^2, w, w, 1, w^2, 0, 1, 1, w^2, 0, w, 0, w^2, w^2, w^2, 1, w, 1, w, 0, 1, 1, 0, w, w, 0, 0, 1, 0, w, 1, 0, w^2, 1, 0, 0, w, w^2, w, w^2, w, 1, 0, w, 1, 0, w, w^2, 0, w, w, 1, w^2, 1, w^2, 1, 0, 0, w, 1, w, w^2, 1, 1, 1, 0, w^2, 0, 0, w, w, w^2, w, 1, 0, 0, 0, 1, w^2, w, w^2, w, 0, 1, w, w^2, 1, w, 1, 0, 1, w^2, 0, 0, 0, w, w^2, w, w, 1, 1, w^2, w, 1, 0, w^2, w, w, 1, w^2, 0, 1, 1, w^2, 0, w, 0, w^2, w^2, w, w^2, 1, w^2, 1, w, w^2, w, 1, 0, 0, 0, 1, w^2, w, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [204, 6, 148] Linear Code over GF(2^2) ExtendCode [1] by 1 last modified: 2008-07-29
Lb(204,6) = 147 is found by truncation of: Lb(205,6) = 148 BKW Ub(204,6) = 150 follows by a one-step Griesmer bound from: Ub(53,5) = 37 is found by considering shortening to: Ub(52,4) = 37 is found by considering truncation to: Ub(51,4) = 36 LMH
LMH: I. Landgev, T. Maruta, R. Hill, On the nonexistence of quaternary [51,4,37] codes, Finite Fields Appl. 2 (1996) 96-110.
Notes
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