lower bound: | 96 |
upper bound: | 96 |
Construction of a linear code [132,5,96] over GF(4): [1]: [131, 5, 96] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, w, w^2, 0, w^2, 0, w, 0, w, w^2, 0, w, 1, w^2, 0, 1, 1, w, w^2, 1, w^2, w, 0, w, 0, w, w^2, 0, 1, 0, 1, w^2, 0, 1, 0, w, w^2, 0, 1, 1, w, 1, 0, 1, w, 0, w, w^2, w, w^2, w, w^2, w^2, 0, 1, w^2, w, w^2, w, w^2, 0, 1, 1, 1, w^2, 0, 1, 0, w^2, 0, 1, w, w^2, 0, w^2, 0, 1, 1, w, w^2, 0, w^2, 0, 1, w, 1, 1, w, w^2, 1, w^2, 0, w, 1, 0, w, w^2, 0, w^2, 0, w, 1, 1, w, w, w^2, 0, w, 0, 1, w, w, w^2, w, w^2, w, w^2, 1, w, 1, 0, 1, w, 0, 0, 1, w^2, 0, 0, w^2 ] [ 0, 1, 1, 1, 0, 0, w, w, w^2, w^2, w^2, 0, 0, 1, 1, w^2, 0, 1, 1, 1, w, w, w^2, 0, 1, w, w, w, 0, 0, w, w, w, w^2, w^2, 0, 0, 0, w, w, w^2, w^2, 0, 1, 1, 1, w^2, w^2, w^2, 0, 1, w, w, w^2, 0, 1, 1, w^2, w^2, 0, 0, 1, 1, w^2, 0, 0, 1, 1, w, w, w^2, 0, 0, 0, 1, 1, w^2, w^2, 0, 1, 1, w, w, 0, 1, 1, w, w^2, w^2, w^2, 0, 1, w, w, w^2, 0, 1, 1, w, w, w^2, w^2, 0, 1, w, w^2, w^2, 0, 0, 1, 1, w, w^2, w^2, 0, 0, 1, 1, w, w, w^2, 0, 0, 0, 1, w^2, w^2, w^2, 0, 1, w ] [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, 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, 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, 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^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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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]: [132, 5, 96] Linear Code over GF(2^2) PadCode [1] by 1 last modified: 2001-12-17
Lb(132,5) = 96 is found by lengthening of: Lb(131,5) = 96 BDK Ub(132,5) = 96 follows by a one-step Griesmer bound from: Ub(35,4) = 24 follows by a one-step Griesmer bound from: Ub(10,3) = 6 GH
GH: P.P. Greenough & R. Hill, Optimal linear codes over GF(4), Discrete Math. 125 (1994) 187-199.
Notes
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