lower bound: | 144 |
upper bound: | 144 |
Construction of a linear code [196,5,144] over GF(4): [1]: [200, 5, 148] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, w^2, 0, 1, w, w, 1, w, 0, 0, 1, w^2, 1, w^2, w, w, w^2, 0, w, 1, 0, w^2, 1, w, w^2, 1, w^2, w, 0, 0, 1, w, w^2, w, w^2, 0, 1, w^2, w, 1, 1, w, w^2, 1, w^2, 1, 0, 0, 1, w^2, 1, 0, w, w^2, 0, 1, w^2, 0, 0, w, w^2, w^2, w, w, 0, 1, w^2, 0, w, 1, 0, w, w^2, 1, 1, 0, 1, w, w^2, 1, 0, w^2, w, w, 0, 0, 1, w, w^2, 0, w^2, w, 0, w, w^2, w^2, w, w^2, w, 1, 0, 0, w^2, 1, 0, w^2, w, 0, 1, w^2, 1, 0, 0, w, w^2, 1, 0, w, w^2, 0, w^2, w, 1, 0, 1, w, w^2, 1, w^2, w, 0, 1, w, 0, 1, w^2, 0, w^2, w, w^2, 0, w^2, w, 1, 0, 1, w^2, w, w^2, 0, w^2, w, 1, 0, 0, 1, w^2, 1, w, w^2, w, 1, 1, w^2, w, w^2, 1, w^2, w, 0, 0, 1, w^2, 0, w^2, w, w, 1, 0, w^2, 0, w^2, w, w^2, 0, 1, 1, 0, 0, 1, 0, w^2, w, w, w^2, 0, w^2, 1, 0 ] [ 0, 1, w, 0, 1, w, 0, w^2, 1, w^2, 0, 1, w^2, 0, w, w^2, 0, 1, w, 1, w, 0, w^2, 0, 0, 1, w^2, 0, 1, w^2, 0, 1, w, w, w^2, 1, w, w^2, 0, 1, w, 1, w, w^2, 0, 0, w, w^2, 0, 1, w^2, 0, 1, w^2, 1, w, w^2, 0, w^2, 0, w, w^2, w, w^2, 0, w, w^2, 0, 0, w, 0, 1, 0, 1, w^2, w, w^2, 1, w, w^2, 0, 1, w, w^2, 0, w, 0, 1, w, 1, w, 0, 1, 0, w, w^2, w, w^2, 1, 1, w, w^2, 0, w^2, 0, 1, w, w^2, w, w^2, 0, w, w^2, 0, w, w^2, 0, 1, w^2, 1, w, 0, 1, w, 0, 1, w, w^2, 0, w, 0, w, w^2, 1, w^2, 1, w^2, 1, w, 0, 1, w, 0, 1, w, w^2, 0, w, 0, 1, w, 0, 1, w, w^2, 0, 1, w^2, 0, 0, 1, 1, 1, 0, w, 0, 1, w^2, 0, 1, w^2, 0, 1, w^2, 1, w, w^2, 1, w, w^2, w^2, 1, w, w^2, 1, w, w^2, w, w^2, 0, 1, 1, w, w^2, 0, 1, w, 0, w, w^2 ] [ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2 ] [ 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, 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, 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, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2 ] [ 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, 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 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [196, 5, 144] Linear Code over GF(2^2) Puncturing of [1] at { 197 .. 200 } last modified: 2001-12-17
Lb(196,5) = 144 is found by truncation of: Lb(200,5) = 148 Bo1 Ub(196,5) = 144 follows by a one-step Griesmer bound from: 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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