lower bound: | 163 |
upper bound: | 165 |
Construction of a linear code [224,6,163] over GF(4): [1]: [225, 6, 164] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, w^2, 0, 0, 1, 0, w, 1, w^2, w^2, 1, 1, 0, w^2, w^2, 1, w, w^2, 0, 0, w^2, w, 1, 0, w^2, w, w, 1, 0, w^2, w^2, 0, 1, 1, w, w^2, w^2, w^2, 0, 1, 0, 0, 0, 0, w, w, 0, w, w, w^2, w, 1, 0, w, w^2, w, w, 1, w^2, w^2, w^2, 1, 0, 1, w, 0, 0, 1, w, w^2, 0, w, 1, 0, 0, 1, w^2, 0, w, w, w^2, 1, 1, 1, 1, 0, w^2, 0, w^2, w^2, 1, w^2, w^2, w, w, 1, 1, w^2, 1, w^2, 1, w^2, 0, 1, w, w, w^2, w, 0, w, 1, 1, w, 0, w^2, w^2, 1, 0, w, w, w^2, 1, 0, w^2, 1, 1, w^2, 1, 0, w, 1, w^2, 0, w, 1, w^2, w, 0, 1, 1, w, 0, w, 1, 0, w^2, 1, w^2, 0, w, w^2, 1, 0, w, w, 1, w, 0, 0, w^2, 0, 0, w^2, w^2, 0, 0, 1, 1, w^2, 0, 0, w^2, 1, w^2, w, w^2, w^2, 1, 0, w, 1, w^2, w^2, w^2, 0, 0, w, w, w^2, w^2, 0, w, 1, w, w, w, w^2, 1, 0, w, w, w, w, 1, 1, w, w^2, 0, w^2, 0, w, 1, w^2 ] [ 0, 1, 0, 0, 0, 0, 1, 0, 0, w, 0, 0, w^2, w, 0, w, w, 0, w, 0, 1, w^2, w^2, 1, w, w^2, w^2, 0, 1, 0, w^2, w, 1, 0, w^2, 1, 0, 1, w^2, 0, w, w, w, w, w, 1, w^2, 1, 0, w^2, 0, w^2, 0, 0, 0, 0, 0, 1, w^2, w^2, 1, 1, w, 0, 1, w, w, w, 0, 1, 1, 1, 1, 0, w^2, 0, 1, w^2, w^2, 1, 0, 0, w, 0, 1, 1, 1, 1, 1, 1, 0, w^2, 0, w, 1, 1, w^2, w^2, 1, w, w, w^2, w^2, 1, 1, 1, 1, 0, w^2, w^2, w^2, 0, 0, 1, w^2, 0, w^2, w, w, 0, w^2, w, 1, w, w, w, w, w, w, w, 1, w, 1, 0, w^2, 1, w^2, w, 0, w^2, w, 1, 0, w^2, w, w, 1, 0, w^2, 1, w^2, 1, w^2, 0, w, 0, w^2, 1, w, 0, 0, w^2, w, w^2, w^2, w^2, 0, 0, w, 0, 1, w, w^2, 0, w^2, 0, 1, 0, 1, w^2, w^2, 1, w, w, w^2, 0, w^2, 1, 0, w, 1, w^2, 0, w, 0, w^2, w, w^2, 1, w, w^2, w, 1, w^2, 1, 0, w^2, 0, w^2, w^2, w^2, 1, w^2, 0, w, w, w^2, w, 0, 1, w^2, w^2, 1, w, 0 ] [ 0, 0, 1, 0, 0, 0, w, 0, w^2, w, w, 0, w, w, 1, w, w, 0, w, w, 0, 0, 0, 1, w^2, w^2, 1, 1, 1, 1, w, 1, 0, w, 1, w^2, w, 0, w^2, w^2, 1, w^2, 1, 0, w^2, 1, 1, w^2, 1, w^2, 1, 0, 1, w, w^2, 0, 0, w^2, 1, w, w^2, 1, 1, 1, w, 0, 1, w, 0, w, 0, w, w, w^2, w, 1, w, w^2, 1, w^2, 1, w^2, w, w^2, 1, 0, 1, w^2, 0, w, w^2, 1, 1, w^2, 0, w, 0, w^2, w^2, 1, w^2, 0, w^2, w^2, w, 1, 0, w^2, w, w, 1, 0, 1, w, 1, 0, w^2, w^2, w^2, 1, w, 0, 0, 1, w, 0, 0, w^2, 0, 0, w^2, w^2, 1, w, 0, w^2, w, 1, w, 0, w^2, 1, w, 0, w^2, w^2, 1, w, 0, 1, 0, w, 0, 0, 0, 0, 0, 0, w, w, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, w^2, w, 0, 1, w, w^2, w, 1, 0, w^2, w, 1, w, w, w, w^2, w, 1, 0, w, 0, 1, w^2, w, 0, w^2, 1, 0, w, 1, w^2, w, 1, 0, w^2, w^2, w, 0, w^2, 1, w^2, w^2, 1, w, 0, 1, w, 1, 0, w^2, 1, w^2, 0, 1, w ] [ 0, 0, 0, 1, 0, 0, w^2, w^2, 0, w^2, 0, w, w^2, 1, 0, 1, 1, 1, 1, w^2, 1, w^2, w, 1, 0, 1, w, 1, 0, 1, 1, w^2, 1, w, 1, 1, 1, w, w^2, 0, 0, w, 1, 0, w^2, w, w^2, w^2, 0, 1, 1, w^2, 1, w, w^2, 0, 1, w^2, w^2, 0, w^2, 1, w, 0, w^2, w, w^2, 0, w^2, 0, w, 0, 1, 1, w^2, w^2, w, 1, w^2, w^2, 0, w, 1, w, 1, 0, 0, w, 1, w^2, w^2, w, w, w, w, 0, 0, w^2, 0, 1, w^2, 1, w, 0, w, 1, 0, w, 0, 0, w, 0, 1, w, w^2, 1, 1, 0, 1, w, w^2, w^2, 0, w, 1, w^2, w^2, 0, w^2, w^2, w^2, 1, w^2, 0, w, w, 0, w, w, w^2, 1, 0, w, w^2, w, w, w, 0, w, 1, w^2, w^2, w, 1, w^2, 1, w, 0, 1, w^2, 1, w, w, w^2, 0, 0, w^2, w, 0, w, 1, w^2, 1, w^2, w^2, 1, w, 0, 0, 1, 1, 0, 1, 1, 0, w, 1, 0, 0, 0, w, 1, 0, w^2, w^2, w^2, 0, 0, 1, 1, w, w, w, 1, 0, 1, 0, 1, 1, w^2, 0, 0, 0, 0, 0, w, 1, 0, w, w^2, w^2, 0, w, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, w^2, 0, w^2, w^2, 1, w^2, 0, 1, w^2, 0, w, 1, 0, w^2, 0, 1, 1, 1, w, w, 1, 0, w, 1, 1, 0, w^2, 1, 1, 0, w, 1, 1, 1, w^2, 1, w^2, 0, w, w^2, w^2, w^2, w^2, w, 1, 1, w, w^2, 0, w, w^2, 0, 1, 1, 0, 0, 1, w, w, w^2, 1, w, w^2, w, 0, w^2, w^2, w, 1, 0, w^2, 0, w^2, w, 1, w^2, 1, 1, w^2, w^2, w^2, w^2, w^2, 1, 0, 1, 1, w^2, 1, 0, 0, 1, w, 0, w, w, w^2, w, 1, 0, w, w^2, 1, 1, 0, 1, w, w^2, 0, 0, w, w, w^2, w, w, 1, w, w, w^2, w, 0, 1, 1, w, 0, 1, w, 1, w, w^2, 0, 0, w, w, w, w^2, w, 1, w^2, 0, 1, 1, w, w^2, 0, 0, w, w^2, w, w, w^2, w^2, w, w, 0, w^2, 0, w^2, 1, w, 1, 1, w^2, w^2, w, w, 0, 0, 0, w, w, 0, 0, 0, 0, w^2, w^2, w, w, w, w, 1, w, w^2, 0, 0, 0, 0, w^2, 0, 0, w^2, 0, w^2, 1, w, 0, 1, 0, w^2, w, 1, 1, 1, w, w^2, 0, 1, w^2, 0, 1, w ] [ 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, w, 1, w, w, 0, w, 1, 1, w^2, 0, w, 1, 0, w, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, 0, 0, 1, w, 0, 0, 1, w^2, 0, 0, 0, w, 0, w, 0, w, w^2, w^2, w^2, w^2, w, 1, 1, w, w^2, 0, w, w^2, 1, 0, 0, 1, 1, 0, w^2, w^2, w, 0, w^2, w, w^2, 1, w, w, w, 1, 0, w^2, 0, w^2, w^2, 0, w, 0, 0, w, w, w, w, w, 0, 1, 0, 0, w, 0, 1, 1, 0, w^2, 1, w^2, w^2, w, w, 1, 0, w, w^2, 1, 1, 0, 0, w^2, w, 1, 1, w^2, w^2, w, w^2, w^2, 0, w^2, w, w, w^2, 1, 0, 1, w, 0, 0, w^2, 0, w^2, w, 1, 1, w^2, w^2, w^2, w, w^2, 1, w^2, 0, 1, 1, w, w^2, 0, 0, w, w, w^2, w^2, w, w, w^2, w^2, 1, w, 1, w, 0, w^2, 0, 0, w, w, w^2, w^2, 1, 0, 0, w, w, 0, 0, 1, 1, w, w, w^2, w^2, w^2, w^2, 0, w^2, w, 1, 1, 1, 1, w, 1, 1, w, 1, w, 0, w^2, 1, 1, 1, w, w^2, 0, 1, 0, w^2, w, 1, 1, w, 1, 0, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [224, 6, 163] Linear Code over GF(2^2) Puncturing of [1] at { 225 } last modified: 2006-09-17
Lb(224,6) = 163 is found by truncation of: Lb(225,6) = 164 Koh Ub(224,6) = 165 follows by a one-step Griesmer bound from: Ub(58,5) = 41 is found by considering shortening to: Ub(57,4) = 41 is found by considering truncation to: Ub(56,4) = 40 HLa
Koh: Axel Kohnert, email, 2006.
Notes
|