lower bound: | 105 |
upper bound: | 106 |
Construction of a linear code [144,5,105] over GF(4): [1]: [147, 5, 108] 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, w^2, 0, 1, 0, 1, w^2, w, 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, 1, w^2, 0, w, 0, 1, w, 1, 0, w^2, w, 0, 1, w^2, w, 0, 0, 1, w^2, 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, 0, 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, w^2, 0, 1, 0, 1, w, w^2, 0, 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, w^2, 1, 0, w, w, w^2, 0, w, w^2, w^2, w, 1, 0, 0, 1, w^2, w, w^2, 1, 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, w, 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, w^2, 0, 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, 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^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, 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, 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, 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^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, 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, 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, 0, 0, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [144, 5, 105] Linear Code over GF(2^2) Puncturing of [1] at { 145 .. 147 } last modified: 2001-12-17
Lb(144,5) = 105 is found by truncation of: Lb(147,5) = 108 Bo1 Ub(144,5) = 106 follows by a one-step Griesmer bound from: Ub(37,4) = 26 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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