lower bound: | 89 |
upper bound: | 96 |
Construction of a linear code [136,9,89] over GF(4): [1]: [137, 9, 90] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, 0, 0, w, w^2, 0, 1, w^2, 0, 1, 1, w^2, w, 0, 1, w, w^2, w^2, 1, w^2, 1, 0, w^2, 0, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w, 0, w^2, 1, w^2, w, 1, w, 1, w^2, w, w, w^2, w^2, 0, w, 0, 1, 1, 0, w, w, 0, 0, w, w^2, w^2, 0, 0, w^2, w^2, 0, w^2, 0, 1, 0, 0, 0, w^2, w^2, w, 0, 0, 0, 1, 0, w, 1, w^2, 0, w^2, w, 1, w^2, w, w^2, 0, 1, w, w, 1, 1, 0, w, w, 0, 0, 1, w, w^2, 1, w, w^2, 1, 0, w, w^2, 0, w, 1, w, w, w^2, w, 1, 0, w^2, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w, w^2, w^2, 1, w, w^2, w, 1, w, 1, w^2, 0, w, 1, w^2, 1, w, w^2, w^2, 1, w^2, 1, w^2, 0, 0, 0, w, 1, 0, w^2, w^2, w^2, 0, 0, 1, 1, w^2, 0, 0, 0, w^2, w, w^2, 1, w, w^2, w, w, 0, 0, w, w, w, w^2, w^2, w^2, 0, 1, w^2, w, 1, w, 0, 0, 1, 1, 1, 0, 1, w^2, 0, w^2, 0, w^2, 0, w, 0, w, 1, w^2, 0, w, 1, w, 0, 0, 1, 1, 0, 1, 0, w, w, 0, w, w, w, w^2, 0, 1, 1, w^2, w^2, 1, w^2, 0, 1, 0, 1, 1, w, 1, 1, 0, w^2, w^2, 1, 0, w^2, w^2, 0, 0, 1, 0, w^2, 0, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, 1, w^2, 1, w^2, 1, w^2, w^2, w^2, w^2, 1, w^2, 1, 1, 0, 1, w^2, 1, w^2, 0, w, 1, w, 0, w, 1, w^2, 1, w^2, w^2, w^2, 0, 0, w, 1, w, w, w^2, 1, 0, 0, w, 1, 0, 1, 1, w, 0, w, 0, 1, 1, w, w, 0, w^2, w, 1, w^2, w^2, 0, w^2, w^2, w^2, w^2, w, w, w, 0, w, w, w^2, w^2, 1, 0, w^2, w^2, w^2, 1, 0, w, 0, w^2, w, 1, w, 0, w^2, 1, 1, w^2, 1, w^2, 1, 0, w, 0, 0, w^2, w, 1, 1, w, 1, 1, 1, w^2, 0, 1, 1, 1, 1, 1, w, 1, 1, w^2, 1, 0, 1, 1, 1, 1, 0, w, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 1, 0, 1, w^2, w^2, 1, 1, w^2, 1, 0, 0, 1, 0, w^2, 1, w^2, 1, w, w^2, w, w^2, 0, w, 1, 1, 1, w, 1, w^2, 0, w^2, w^2, w^2, w^2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, w, w, 0, w, w^2, 0, 0, 1, w, w, 0, 0, w, w, w, 0, 0, 1, w, w^2, 1, w, 1, 0, w, 0, 0, 0, 0, 0, w^2, 0, w^2, 0, w, w, 0, w, w, 0, w, 0, w^2, 0, w^2, w^2, w, 0, 1, w^2, w^2, 1, 1, 1, 0, w, w, 1, 1, w^2, 1, 1, w^2, w, 0, 0, w^2, w, w^2, w^2, 1, w, 1, 1, w, 1, 1, 1, 0, w^2, 0, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, w^2, 0, 1, w, w, w, 0, w, w^2, w^2, w, 0, 0, w, w^2, w^2, 1, w, w^2, 1, 0, 1, 1, w^2, w, w, w^2, 0, 0, w^2, 1, 1, 1, w^2, w, 1, w, 1, 1, 1, w^2, w^2, 0, w, 1, 1, w^2, w^2, 0, 0, 1, w, 0, 0, 1, w, w, 1, 0, 1, 1, w^2, 1, w^2, 0, 1, 1, 0, 1, w, w^2, 1, 0, w^2, 0, 0, w, w, 0, w, 0, w^2, 0, 1, w, w, 1, 0, 1, w, w^2, w^2, 0, w^2, 0, w^2, w, 0, w, 0, 1, 1, 1, w, w^2, 0, 0, w^2, w^2, 1, 1, 1, 1, 1, w, w, w, 0, 0, 1, w, w^2, w, w, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w, w^2, w^2, w^2, w, 1, 1, 1, w^2, 0, 0, 0, w, w, w^2, w^2, 0, w^2, w^2, 1, 1, 1, w, w^2, w^2, 1, w^2, 0, 0, 0, 1, w, 1, w, w, 0, w, w, 0, 0, w^2, w, 1, 1, 1, 0, w^2, 0, 0, w, w, 0, w, 0, 1, w^2, w^2, 1, w, 1, w^2, 1, 0, w, w^2, 0, 0, w, w, w, 1, 1, 1, 0, 0, 0, w^2, 1, w^2, 1, w, w, w^2, 1, w, 0, w, 1, w, w^2, 0, w, w^2, 0, w, 0, w, w, 1, w, 1, w^2, 0, 1, 0, w^2, 0, 1, 0, w^2, w^2, 0, 0, w, 1, w, w, w, 0, w^2, w, w^2, w^2, 1, 0, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, w, 1, w, 1, 1, w, w, 0, 1, w, 1, w, 1, w, w^2, 0, 0, 1, 0, 1, w, 1, 1, 0, w^2, 0, 0, 0, 1, w^2, w^2, w^2, w, w^2, 1, w, 0, w^2, w, 0, 1, w, 1, w^2, 1, w, 1, 0, w, 1, w^2, 0, w^2, w^2, w, 0, w, 1, w^2, 0, w, w^2, w^2, 0, 1, w^2, 1, w, 0, w, w^2, 0, 0, w^2, w^2, 1, w^2, w^2, 1, w, w^2, 1, 0, w, 0, w, 0, 0, 1, w, 0, 1, 1, w, 0, w^2, 0, 1, w^2, w^2, w^2, 1, w, 0, w^2, 1, 0, 0, w^2, 0, w, 0, 0, w, w^2, 0, 0, w, w, w^2, 1, w^2, 0, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w, w, 1, 0, w, 0, w, 1, 1, 1, w, 1, 1, 1, 0, w^2, w, 0, w, 0, w^2, w^2, 1, 0, w^2, w, w^2, 0, w^2, w, w^2, 0, 0, w^2, 0, 1, w, w^2, w, 0, 0, 1, w^2, 0, w^2, 0, w, 1, 1, 0, w, w, 1, w, 0, w, 0, w^2, w, w, 0, w^2, w, 0, 0, w^2, 0, 0, w, 1, 0, 0, 1, 0, w, w, w^2, 1, 1, w, 0, 0, 1, 1, 1, 1, w, w, w^2, w, w, w^2, 1, w^2, w^2, w^2, 0, 0, 0, 1, w, w^2, 1, 0, w, 1, 0, 0, w, 1, 0, w, 1, w, w^2, w, 0, w^2, 1, 1, w, 1, 0, 0, 1, w^2, w, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 0, w^2, w, w, w, w, 1, w, 0, 0, 0, w, w^2, 1, 0, 0, w^2, 0, w, 0, 0, w^2, w, 0, 0, 0, w, 0, 1, 0, w^2, 0, 0, w, 1, 0, 1, w^2, w, w^2, w, 1, 0, w, 1, w, w^2, w^2, 0, w, 0, w^2, 1, 1, w, w, w^2, w, 1, w^2, w^2, 0, w, 1, w, w^2, w, 1, 1, 0, 0, 1, 1, w, 1, 1, 0, 1, w^2, 1, w^2, w^2, w, w^2, w^2, 1, w, 1, w^2, w^2, w^2, 1, 0, w, 1, 1, 0, w^2, w, w, 0, w, w^2, 1, w^2, w, w^2, w^2, w, 1, w, w, w, w, w, w, 1, w, w^2, 0, w, 0, w, w^2, 1, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [136, 9, 89] Linear Code over GF(2^2) Puncturing of [1] at { 137 } last modified: 2009-12-14
Lb(136,9) = 88 is found by taking a subcode of: Lb(136,10) = 88 DaH Ub(136,9) = 96 follows by a one-step Griesmer bound from: Ub(39,8) = 24 follows by a one-step Griesmer bound from: Ub(14,7) = 6 is found by considering shortening to: 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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