lower bound: | 102 |
upper bound: | 103 |
Construction of a linear code [140,5,102] over GF(4): [1]: [142, 5, 104] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 1, w, w^2, 0, 1, 0, w^2, 0, 1, w, w^2, 1, 0, w^2, w, 0, w, 0, 1, w^2, w, 1, w^2, w, w, 1, w^2, 0, 0, w, w^2, 0, 1, 0, 1, w^2, w, 1, 1, w^2, 0, w^2, w, w^2, 1, 0, 1, w, w^2, w, 0, w^2, w^2, 1, 1, 0, 1, 0, w, 1, 0, 0, 1, w, w^2, 0, w^2, 0, 1, w^2, w, 1, 0, w^2, 1, 0, w^2, w, w^2, 0, w, 0, 1, w, 1, 0, w^2, w, 0, 1, w^2, w, 0, 0, 1, w, 0, 1, w^2, w, w^2, 1, w, w^2, 1, 1, 0, 1, 0, w, w^2, w^2, w^2, w, 0, w, w^2, 0, 1, w^2, 0, 1, w^2, w, 1, 1, 0, w, 1, 0, w, w^2, 0, w^2, w^2, w^2, w, w^2, w ] [ 0, 1, 0, 1, 1, 0, w^2, w^2, w, 1, 0, w, w, w^2, 0, 1, w, 0, w^2, 1, w^2, w, 1, 0, w^2, w, w^2, w, 1, 1, w, w^2, 1, 0, 0, 1, 0, 1, w, w^2, w^2, w, 0, 1, w, w, w^2, 1, w^2, w, 1, 0, 0, w^2, 0, w^2, 1, w^2, w, 0, 1, w^2, 0, 1, 0, 1, w, w^2, w^2, 1, 0, 1, w, w^2, w^2, w, 0, w^2, w, 1, w, 1, 0, w, w, w^2, 0, w, w^2, w^2, w, 1, 0, 0, 1, w^2, w, w^2, w^2, 1, 0, w^2, w, 1, w, w^2, w, 0, 1, w, w, w^2, 1, 1, w, w^2, w, 0, 0, 1, w, w, w^2, 0, 0, w, w^2, 1, w, w^2, 0, 1, 0, 0, 1, w^2, 0, 1, w, w^2, 0, 1 ] [ 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 1, w, 0, 1, 1, 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, 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, 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, 0, 1, 0, 1, w, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [140, 5, 102] Linear Code over GF(2^2) Puncturing of [1] at { 141 .. 142 } last modified: 2003-03-12
Lb(140,5) = 102 is found by truncation of: Lb(142,5) = 104 Bo1 Ub(140,5) = 103 follows by a one-step Griesmer bound from: Ub(36,4) = 25 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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