lower bound: | 76 |
upper bound: | 78 |
Construction of a linear code [108,6,76] over GF(4): [1]: [108, 6, 76] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^2, w, w^2, w, 0, 0, w^2, 0, w, 0, w^2, w, 0, 0, 0, 0, w^2, 0, w, 0, w^2, 1, 1, 1, w^2, 0, w, 0, 1, 1, w^2, 1, 1, 1, w, 0, 1, 0, w^2, 0, w^2, 0, 0, 0, w, w, 0, 1, 0, 1, w, 1, w^2, w, w^2, w, w, w^2, 1, w^2, w, 1, w^2, 1, w, 0, 1, w^2, 1, w, w, 0, 0, 1, 1, 0, w^2, 1, w^2, 0, 1, 1, w, w, w^2, 1, 1, w, 1, w^2, w^2, 1, w^2, w, w^2, 1, w, w, w^2, 1, w^2, w ] [ 0, 1, 0, 0, 0, 0, w, w^2, 0, 0, w^2, w, 0, w^2, 0, w, w, w^2, w^2, 0, w, 0, 0, 0, 0, 0, 1, 1, w^2, 1, 0, w^2, w, w, 1, 0, 1, w^2, w^2, 0, w, w, 0, 1, 1, 1, 0, w^2, 0, 1, w, 0, 0, 0, 1, 0, 1, w, w^2, 1, 1, w, 1, w^2, 1, 1, w, w, w^2, w, 0, w, 0, 0, 1, 1, 0, w, 1, 1, w^2, w^2, 1, w^2, 0, w^2, 1, 1, w, 1, w^2, w^2, w, 1, w, w^2, 1, 1, w, w^2, 1, w^2, w, w^2, w^2, w, w, 1 ] [ 0, 0, 1, 0, 0, 0, 1, 1, w, w^2, w, w^2, 0, 0, 0, 0, 0, 0, 0, w^2, 0, w, 0, w^2, 0, w, 1, w^2, 1, w^2, 1, 1, 0, w, 0, 1, 1, 1, 0, w^2, 0, w, 1, 1, 0, w^2, 0, 0, w^2, 0, 0, w, w, 1, 1, 0, w, w, w^2, 1, w^2, 1, w, w^2, w, w^2, 1, w, w^2, 0, 1, 1, w, w^2, w, 0, 1, 1, w, 0, w^2, w^2, 0, 0, 1, 1, 1, 1, w, w, 1, w^2, w, 1, 1, 1, w^2, w^2, w^2, w^2, w, w, 1, w, 1, w^2, w, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, w, w, w^2, w^2, 0, 0, w, w, w^2, w^2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 1, 1, 1, w^2, 0, 0, w, 0, 0, 1, 1, 1, 1, w, w^2, 1, 1, 1, w, w^2, 0, 0, 0, w, w, w, w, w^2, 0, 1, 1, 1, 1, w, 0, 1, w^2, w^2, w^2, w^2, 1, 1, 1, w, w^2, w^2, 1, w, w, 1, 1, w^2, w, 1, w^2, w, w^2, w^2, w, w^2, 1, w ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w, w, w^2, w^2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, 1, 1, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 1, w, w, w^2, w^2, 1, w, w, w^2, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2004-04-21
Lb(108,6) = 76 BKW Ub(108,6) = 78 follows by a one-step Griesmer bound from: Ub(29,5) = 19 is found by considering truncation to: Ub(26,5) = 16 BGV
BKW: Michael Braun, Axel Kohnert & Alfred Wassermann, Optimal linear codes from matrix groups, preprint, Mar 2004, and Construction of (sometimes) Optimal Linear Codes, email, Mar 2005.
Notes
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