lower bound: | 130 |
upper bound: | 135 |
Construction of a linear code [188,8,130] over GF(4): [1]: [190, 8, 132] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, 1, 0, w, 0, w^2, w^2, 0, w, 1, 1, w^2, w, w, 1, 0, w, 0, 1, 1, 1, 0, w^2, w, w^2, w^2, w, w, w, 1, w, 1, w, 1, w, 1, w, w, w, w^2, 1, 1, w^2, 0, 1, w, w^2, w, w^2, w, w^2, w, w, w, 0, 1, 0, w^2, w, w^2, w, 0, w^2, w, 1, w, w^2, 1, 0, 0, 0, w^2, w^2, w, w^2, w^2, 0, w, 1, w^2, 1, w, w, 0, 0, 0, w, w, 0, w, w^2, w^2, w, w^2, 0, 1, 1, w, w, 0, 0, 0, 0, 0, w^2, w^2, 0, w, w^2, 0, 1, 0, w^2, w, 1, w^2, w^2, 1, 0, 1, w^2, 0, w^2, w, 0, 1, w, 0, 1, w^2, w^2, w, 1, w, w^2, w, w^2, 0, 0, w, 0, 0, w, 1, 0, 1, w, 0, w, w, w^2, 1, 0, w, w, 0, w^2, w, 0, w^2, w, 0, w, 1, w^2, w^2, 1, w, w^2, w^2, w^2, w^2, 0, w^2, 1, w^2, w^2, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 1, w^2, 0, 0, 1, 1, 1, 0, w, 0, 1, w, 0, 0, 1, w, 0, w, w^2, 0, w^2, 0, 1, w^2, 1, w, w^2, w^2, w, w, 0, w, 1, w, w, 1, w^2, 1, w, w, w^2, 0, w^2, w, w, 0, w^2, w, 1, 0, 0, w, 1, w, w, 1, 1, w^2, w^2, 0, 0, 1, 1, w, 1, w^2, w, 1, 0, 0, w^2, 1, 1, w, w^2, w^2, w^2, w, w, w, w^2, 0, w, 1, 1, 1, 0, 1, 0, 1, w, 1, w, 1, 0, w, 1, 1, 1, w^2, w, w, 0, w, w^2, w^2, w, 1, w^2, 1, 1, 1, w^2, w^2, 0, 1, 1, w^2, w, 0, 1, w^2, w, 0, w, 1, 1, 1, w^2, w, w, 0, 1, w^2, 0, 1, 1, w, 1, 1, w^2, 1, 0, 0, 1, 1, 1, 0, w, w, w, 0, w, w, w^2, w^2, 0, w, w, w, 1, 1, w, 1, w^2, 0, 0, 1, 1, 0, w, w^2, w^2, w^2, 1, w^2, w^2, w, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 0, w, w, w, w^2, 0, w^2, 0, w^2, w^2, 0, 0, w^2, 1, w, w, w^2, 1, w^2, 0, 0, 0, w, w^2, w, w^2, 1, 1, w^2, w^2, 0, w^2, w^2, 1, w, w^2, w^2, 0, w^2, 0, 0, 1, w, 0, w^2, w^2, w, 1, w^2, w, 1, 1, w^2, w, w^2, w, w^2, w^2, 0, w, w^2, 0, w, 0, w^2, w, 0, w^2, 0, w^2, w, 1, w^2, 0, 0, w^2, 1, 0, 0, 1, w^2, w^2, w, w, 0, w^2, w^2, 0, 0, w^2, w, 1, 1, w, 1, 0, 1, 1, w, 1, w, 1, w, w^2, w, w, 1, w^2, w, 0, 1, 0, 1, w, w, 1, 0, 0, w^2, w, w, 1, 0, 1, w, w, w, 0, w^2, 1, w^2, 0, w^2, w^2, 1, 1, 0, 0, w^2, w, 1, 1, 1, w^2, w^2, w^2, 0, 0, w^2, w^2, 0, 1, 0, w, 0, 0, 0, w^2, 1, w, w^2, 1, 1, 0, 0, 0, 0, 0, 1, w, w^2, w, w, 1, w, w, 0 ] [ 0, 0, 0, 1, 0, 0, 0, w^2, w^2, 0, w^2, w, 0, w, w^2, w, 0, w, 0, 1, w^2, 0, w, w, w, w^2, w, w, 1, 0, 0, w^2, 0, w, w, w, 1, w^2, 0, w^2, 0, w^2, w^2, w, 0, 1, w^2, 1, 0, w, 0, w^2, 0, 0, 0, 1, w^2, w^2, w, 1, 1, w, w, w^2, w^2, 1, w, w, w, 1, w, 0, w^2, 1, 0, w, w^2, 1, w^2, w^2, w, 1, 1, 0, w, w, w^2, w^2, w^2, w^2, 1, w, 0, w, w, 1, 1, w^2, 1, 0, 1, 1, 1, w, w, w^2, 0, w^2, w^2, w, w, 0, w, 0, w, w, w, 1, w^2, w, w^2, w, 1, w, 0, w^2, w^2, w, w^2, 1, 1, 1, w, 0, w, 1, 0, 0, 1, w, 0, w, 0, 1, 0, 0, 1, 1, w, 0, w, w^2, 0, w^2, 1, w^2, 1, w, w^2, 0, 1, 0, w, w, w^2, w^2, 1, 1, w^2, w^2, w, w^2, w^2, w, 0, 1, w^2, w^2, w, w, 1, 0, w^2, 0, 1, w^2, 1, 0, w^2, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, w^2, 0, 1, 0, w^2, w^2, 0, 0, 0, 1, w^2, 1, w, w^2, 0, 1, 0, 0, 0, w^2, 1, 1, w^2, w, 1, 1, w^2, w^2, 0, w^2, w^2, w^2, 0, w^2, 0, w^2, w^2, 0, w, w, w, 1, 0, 1, w, w^2, w, w^2, 1, 1, w^2, 0, 1, 1, 1, 1, 0, w^2, w^2, 0, 1, w, w, w^2, 1, w^2, 0, w, 1, w^2, 0, w, w^2, 0, 0, 0, 0, w, 0, w, 0, 1, w, w^2, 1, 1, w, w^2, 1, 0, 1, 1, 0, w^2, 1, 0, 1, w, w, 1, w^2, w^2, w^2, w^2, 1, 1, w^2, w, 1, w^2, w, 0, w, 0, w, 1, 1, w, w^2, w, w^2, 1, 0, w, w, w^2, 0, 1, w, 0, 0, w^2, 0, 1, w^2, w, 1, 0, 0, 1, 1, 0, 1, 1, w, w, w, 0, w, w, 0, 1, 1, 1, w, 1, 0, 0, w^2, 0, 0, w^2, w^2, w, 0, 1, w^2, 0, w, w, 1, w, 0, 1, 0, 1, w, 0, w^2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, w, w, 0, 1, 0, 0, 1, 0, 1, 0, 0, w, w, 0, 1, w^2, 1, w, 0, w^2, w^2, w^2, 0, w, 0, w^2, 1, w, w, 0, w, w, w, w^2, 0, w^2, w, w, w, 1, w^2, 0, 0, w^2, w, w, w, 1, w^2, w, 1, 0, 0, 0, w, 1, 1, 0, 0, w^2, w, w^2, w^2, w^2, 1, w^2, 1, 0, 0, 1, w^2, 1, 1, w^2, 0, 1, 1, 1, 0, 1, w, 1, w^2, 0, w, 0, 1, 1, 0, 0, w^2, w, 1, 1, 1, 0, 0, 1, 1, w^2, w^2, 1, 0, w, 1, w^2, w, w^2, w, 0, 0, w^2, w, 1, w, w, w^2, 1, 1, w, w, w^2, 1, w, 1, 1, 0, w, w, 0, 0, 1, 1, 0, 1, 0, 1, w, 1, 1, w, 0, w^2, w, 0, w^2, w^2, 0, 0, 0, w^2, w^2, w^2, 1, w, w^2, 0, 1, w^2, 0, 1, 1, w, 1, w, 1, 0, 1, 0, w, 0, 1, 1, w^2, 0, 0, 0, 0, w, w^2, w, w, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, w, w^2, w^2, w, 0, w, w, w, w, w^2, 1, 1, w^2, 0, w^2, 1, 0, w^2, w^2, w, w, w, w, 1, w, w^2, 1, 0, w, w^2, 0, 1, 1, w, 1, w^2, 0, w^2, w, w^2, 0, 0, 0, 0, w^2, w^2, w^2, 0, 1, 0, 1, w^2, 1, 0, w^2, 0, w, w^2, w^2, 1, w, w^2, 1, 1, 0, w^2, 1, 1, w^2, w, 0, w^2, 1, 0, w^2, 0, 0, 0, 0, w^2, 0, 1, 1, 0, w^2, 0, w^2, w^2, 1, w, w^2, 1, 0, w, w^2, w^2, 1, w, 0, 1, w, 0, w^2, w, 0, w^2, 1, w^2, w^2, 0, 1, w, 1, 0, w^2, 1, 1, w, w^2, w, 1, w^2, 0, w^2, 0, 1, w, 0, 1, 1, w^2, w^2, 1, w^2, w, 1, w, 0, w, w^2, 1, w^2, 0, w^2, 0, 1, 0, w, 1, 0, 0, w^2, w, w, 1, w, w, w, w^2, 1, 1, w, w^2, w, 0, 0, w^2, 1, 1, 0, w^2, w, 0, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, 0, w, w^2, w, w, 1, w^2, 1, w^2, w, 1, w^2, 0, w, w^2, 0, 0, w^2, w, 0, w, w, w, w, 1, w, 1, 0, 0, 1, w, 0, w, 1, 0, 1, w, w, 0, w, 1, 1, w, 0, w, 0, 1, w, 0, 1, w, w^2, w^2, w, 1, w, 0, w^2, w^2, 1, 0, w^2, w, w^2, w, 0, w, w^2, 1, w^2, 1, w, w^2, 1, w^2, w^2, 1, w^2, 0, 0, w^2, w, w^2, 0, w^2, w, 0, 0, w^2, w^2, 1, w, 0, w^2, w, 0, w^2, 0, w^2, 1, w^2, 1, w^2, 0, w^2, 0, 0, 1, 0, w, w^2, 0, w^2, 0, 1, w, 0, w^2, 0, w, 1, 1, w, w, 1, w^2, w^2, w^2, w^2, 1, 0, 1, w^2, 1, 1, 0, 0, w^2, w^2, w, 1, w^2, w^2, w^2, w, w^2, w^2, 1, 1, 0, 0, w, 1, w^2, w, w^2, 0, w^2, 1, 0, w, 1, 0, w^2, 0, 0, 0, 0, 1, w, w^2, 0, w^2, w^2, 1, w^2, w, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [188, 8, 130] Linear Code over GF(2^2) Puncturing of [1] at { 189 .. 190 } last modified: 2012-08-21
Lb(188,8) = 128 is found by lengthening of: Lb(187,8) = 128 GW2 Ub(188,8) = 135 is found by considering truncation to: Ub(186,8) = 133 Da1
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
|