lower bound: | 119 |
upper bound: | 120 |
Construction of a linear code [164,6,119] over GF(4): [1]: [165, 6, 120] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, w, w^2, w^2, 1, 1, w^2, 1, 0, w, 0, w, w, w, 0, w^2, w^2, 1, w, w, w^2, w^2, w^2, 1, w^2, 1, w^2, w, w^2, 1, 0, 1, 0, 0, 1, w^2, 1, 1, w, 1, 0, w^2, 1, 0, w, w^2, 1, 0, w, 0, w^2, 1, w, 1, w, 1, w^2, w^2, 0, w, w^2, 0, 0, w, w^2, w, w, w, w^2, 1, w^2, 0, 0, 0, 0, 0, w, 0, 1, 1, w^2, w, w, 1, 1, 0, w, w^2, w^2, 1, 1, w^2, w, 0, w, 0, w, 0, w, 0, w^2, w^2, w, w^2, w^2, w, w^2, w, w^2, 0, 0, w^2, 1, 0, 0, 1, 0, w, w^2, w, w^2, 0, 1, w, 0, 1, w^2, 0, 1, w, 1, w, w, w^2, 1, w^2, w^2, 0, 0, 0, 0, 0, 0, w^2, w^2, w, w, 1, 1, w, 0, w, 1, 1, w^2 ] [ 0, 1, 0, 0, 0, 1, 0, 1, w^2, w, w^2, 0, 1, 1, 0, w, 0, w, 1, 1, w^2, 1, w, w, 0, w^2, w^2, 1, w, w, 1, 1, w, w, w, w, w^2, w, w^2, 1, 0, 1, 0, 0, 1, w^2, w^2, w^2, 0, 1, w^2, 1, w, 0, w, w^2, 1, w, 1, w, w^2, 0, w, 0, 1, w^2, 0, 1, 0, w^2, w, w^2, w, 0, w, w^2, 1, 1, 1, w^2, 0, w^2, w^2, w, w^2, w, 0, w, w^2, w^2, w, w^2, 1, w, 0, 1, w^2, 0, w, 0, 1, w, w, 1, w, 1, w^2, 0, w^2, w^2, w, 0, w, 0, w^2, 1, 1, w^2, 0, 1, 0, w, 1, 1, w, w^2, w, w^2, 1, 1, 0, w^2, w, w^2, w, 0, w, w^2, 0, w^2, w^2, 0, 1, w, 0, 0, 1, w, w^2, w^2, w^2, w^2, 0, 1, 1, w^2, w^2, w, w^2, 0, w, w, 1, 1, w^2 ] [ 0, 0, 1, 0, 0, 1, w, w, 0, w, w, w, w^2, 1, 0, w^2, w^2, 0, 0, 1, w^2, w, w^2, w, 0, w^2, w, w, w, w^2, w, 1, 0, 1, w, 0, w^2, 0, 1, 1, w^2, w^2, w, 0, 0, 1, w, 1, w, 0, 1, w^2, 1, w^2, 1, w, 1, 1, 0, 1, w, w^2, w^2, 1, 1, 0, 0, 1, 0, 0, 1, w^2, 1, w^2, 0, 0, w, 0, 0, w^2, w^2, w^2, 0, w, w, w^2, 0, 1, w^2, w, 1, w, w, 1, w^2, 1, w^2, 1, w^2, w, 0, 1, 1, w, 0, 0, w^2, 1, 1, 1, 0, w, 0, w^2, 0, 0, 0, 1, 0, 1, w^2, w^2, w^2, w, 0, w^2, w, w, 1, w^2, w, w, w, w, 0, w, w^2, w, 0, w, w^2, 1, 1, w^2, 0, w^2, w, w^2, w^2, 0, 0, w^2, 1, 0, w, 1, 0, 0, w, w^2, 1, 0, w^2, w, w^2 ] [ 0, 0, 0, 1, 0, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, w^2, 1, 0, w, 1, 1, w, 0, 1, 0, 0, 1, w, 1, 0, w, 1, w, w^2, 0, w, 0, w, w, w, 1, 0, 0, w, w, w^2, 0, w^2, w, 1, w, w^2, w, w, w, 0, 0, w^2, 1, 1, w^2, 1, w, w, w^2, w, 1, 1, 1, w, w, 1, w, w, w^2, w, w^2, 1, 1, 0, w^2, 0, 1, w, w^2, w^2, w^2, 0, w^2, w, 0, w, w, w, w, 1, 1, 0, 1, 0, w^2, 1, 0, 0, w^2, 0, 1, 0, w, 0, w^2, w^2, w, w^2, w, 0, 0, w^2, 1, 1, w^2, w^2, w^2, w, w, 1, 1, 0, 0, w, w, w^2, w, w^2, 1, w^2, 0, 0, 0, 1, 0, 1, w, w^2, w^2, 0, w, 0, 1, w, 0, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w^2, 1, w, w^2, 0, 1 ] [ 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 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, w, w, 1, w^2, 1, w^2, w, w, w, w, w, w, 1, w^2, 1, w^2, w, w, w^2, 1, w, w^2, w, 1, w^2, w, w^2, w^2, w, 1, w^2, w, w^2, w^2, 1, w^2, w, 1, w^2, w, w^2, 1, 1, 1, w^2, w^2, w^2, w^2, 1, 1, w, w, w^2, w, w^2, w, 1, 1, w, w, w^2, w^2, w, w, w^2, w^2, w, 1, w^2, w^2, w^2, w, w, w^2, w^2, w, w^2, w, 0, 0, 0, 0, 1, w, 1, w, 1, w, 1, w^2, 1, w, 1, w, w^2, w^2, w, 1, w, 1, 1, 1, 1, w, w, w, w, 1, 1, w, w^2, w^2, w^2, 1, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, w, w, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [164, 6, 119] Linear Code over GF(2^2) Puncturing of [1] at { 165 } last modified: 2009-01-27
Lb(164,6) = 117 is found by truncation of: Lb(165,6) = 118 BKW Ub(164,6) = 120 follows by a one-step Griesmer bound from: Ub(43,5) = 30 follows by a one-step Griesmer bound from: Ub(12,4) = 7 is found by considering shortening to: Ub(11,3) = 7 is found by considering truncation 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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