lower bound: | 30 |
upper bound: | 31 |
Construction of a linear code [44,5,30] over GF(4): [1]: [46, 5, 32] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 1, 0, 1, w^2, w, w^2, w, 1, w^2, w, 1, 0, w, w, w^2, 1, 0, w, w^2, 1, 0, 0, w, 0, w, w^2, 1, w, 1, w^2, 0, 1, w, w^2, 0, w, 1, 0, w^2, w, 0, w^2, w ] [ 0, 1, 0, w, 0, w, w^2, 0, 1, 1, w^2, 0, w, w^2, 0, 1, 0, w, 0, 1, w, 1, w, w^2, w, w^2, w^2, 0, 1, 0, 1, w, w, w, w^2, w^2, 0, 1, w^2, 1, w^2, 0, 1, w, w^2, 0 ] [ 0, 0, 1, 1, 0, 0, 0, 1, 1, w, w, w^2, w^2, w^2, 0, 0, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 1, w, w, w^2, 0, 0, 0, 1, 1, w, w^2, w^2, w^2, 0, 0, 1, 1, w, w, w^2 ] [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 ] [ 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 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [44, 5, 30] Linear Code over GF(2^2) Puncturing of [1] at { 45 .. 46 } last modified: 2001-12-17
Lb(44,5) = 30 is found by shortening of: Lb(45,6) = 30 Koh Ub(44,5) = 31 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
Koh: Axel Kohnert, email, 2006.
Notes
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