lower bound: | 83 |
upper bound: | 85 |
Construction of a linear code [120,7,83] over GF(4): [1]: [121, 7, 84] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, w^2, 1, 0, 1, 1, 1, w, 0, 1, 0, w, 1, w, w^2, w, w, w, w, 1, w, 1, w^2, w, 0, w, 1, w^2, 0, w, 1, 0, 0, w, 1, w^2, w^2, 1, 1, 0, w, w^2, w^2, 0, w^2, w^2, w, 1, w^2, w^2, 0, 1, w, 0, 1, w, 1, w, w, w^2, 1, w, 1, 0, w^2, w, w^2, w^2, 0, 0, w, 1, 0, w, w^2, 1, 1, 1, w, w^2, 0, w, w, 0, w^2, 1, 0, w, 1, 1, w, w^2, 0, w^2, w^2, 1, w, 1, 0, 0, w^2, 0, w, 1, 0, w, w^2, 0, w, w^2, w, 0 ] [ 0, 1, 0, 0, 0, 0, w, 1, 0, 0, 1, w, 0, 0, 0, w^2, 0, w^2, w, 0, w^2, w, 0, w^2, w^2, w^2, 0, 1, w, 0, w^2, 0, w, 0, 0, 0, 0, w^2, 1, w, 1, 0, w^2, w^2, w^2, w^2, 1, w^2, 1, 1, 1, w^2, 0, w^2, w^2, 0, w^2, 1, w, 0, w^2, 0, w, 1, w, 0, w, 0, w^2, w, w, 0, w^2, 1, 1, 1, w, 1, w, w, w, 1, w, 0, w^2, w, w, 1, w, w, 1, 0, w^2, w, 0, w^2, w, w^2, w^2, 1, 1, 0, 0, 0, w^2, w^2, 0, w, 0, 1, w^2, 1, 1, w, w, 1, w^2, 0, w, w, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, w^2, 1, w^2, 0, 0, w, 1, 1, 0, 0, 1, w^2, 1, 0, w^2, 0, 1, 0, 0, w^2, w^2, 0, 0, w^2, 1, w^2, 1, w, 0, w, w^2, w, w^2, 0, w^2, w^2, w^2, w, 0, w, 1, 1, 0, 1, w^2, w, 1, w, 0, w, 0, 1, 1, 0, 1, 0, w^2, 1, w^2, w^2, w, w^2, 0, 1, 0, w, 1, w^2, w^2, w^2, 0, 1, 1, 1, 1, w, 1, 0, 1, w, w^2, w, 1, w, 1, w^2, w^2, 0, w^2, w, 0, 1, 0, w^2, 1, w, 0, w^2, 1, w, 0, w^2, 0, w, 1, w, 1, 0, 1, w^2, 1 ] [ 0, 0, 0, 1, 0, 0, 1, w^2, 0, 1, 0, 0, 0, 1, 1, w^2, w^2, w, w, 1, w^2, w^2, w, 0, 1, 0, 1, 1, 0, 1, w^2, w^2, w, 1, w^2, w^2, 0, 0, w^2, 1, 0, w^2, w, w^2, w^2, 0, 0, w^2, 0, 1, 1, 0, w^2, 1, w^2, 0, w^2, w^2, w^2, w^2, w, 1, 1, 0, w^2, w^2, w^2, 1, 0, 1, w^2, 0, 0, 1, w, w^2, 0, 0, w, w^2, w, 1, w, 0, w^2, w, w^2, 0, 1, 0, 0, 1, w^2, 1, w^2, w, w^2, 1, 1, w^2, 0, 1, w^2, w^2, 0, 0, w, w, 0, w^2, 1, w^2, w, w, w, 1, 0, 0, w^2, 0, w ] [ 0, 0, 0, 0, 1, 0, w, 1, 0, w, 1, w, 1, 0, w, 0, w^2, w^2, w, w, 0, 0, 0, w, w^2, 1, 0, w, 1, 0, 0, w, w, w^2, 0, w^2, 0, w^2, w^2, w^2, w^2, w^2, 0, 1, 1, 1, w, 0, 1, w, 1, 0, w^2, w^2, w, w, 0, 0, 1, w, w^2, 1, w^2, 1, w^2, w, 0, w, w, 1, w, w^2, w, w^2, 0, 1, w, w, 0, 1, 0, w, w, w, w, w^2, 1, w^2, w, 1, 1, w^2, w, w^2, w, 1, 0, 0, 1, 0, 0, 0, 0, w^2, w^2, w, w, w^2, 0, 1, w, 0, 1, 0, 1, w, 1, w^2, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 0, w, 1, 0, 0, 0, w, 0, 0, w^2, w^2, 1, 0, 0, 1, 0, 0, 0, 0, w, 1, w, 1, w^2, 1, w^2, 1, 1, w, w^2, w^2, 0, 0, w^2, w^2, w, 0, w^2, w^2, w^2, w, w^2, w, 0, 1, w^2, 0, w, 1, w^2, w^2, w^2, 1, 0, 1, 1, 0, w, w, w, 1, w^2, w^2, 0, w, 1, w, w^2, w^2, 0, 1, 0, w, 0, w^2, 1, w, w, w, w^2, w^2, 0, w^2, w, 0, 1, w, w, w^2, 1, w^2, w^2, 0, 0, 1, 0, w^2, 1, 0, w^2, w, 0, 1, 1, 0, w^2, 1, w, w^2, w, w^2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, w^2, 1, 1, w, w, 1, 1, w^2, w^2, w^2, 1, w^2, 1, 1, w^2, w^2, w, w^2, w, 0, 0, w^2, 0, w^2, 0, 1, 1, w, 0, 0, w, w^2, 0, 0, w^2, 1, w^2, 0, 1, 1, 1, 0, w^2, 1, 0, 1, 1, 1, w^2, w, 1, 1, 0, w, w, w, 0, w^2, 1, 0, w, 1, w, 0, 0, 1, w^2, 0, w^2, w, w^2, 0, 1, w, w, w^2, 0, 1, w, 1, w, 1, w, 0, w, w^2, w^2, 0, w^2, 1, 0, 0, w^2, 1, 0, w, w, w^2, 0, w^2, w, 0, w, 0, 1, w, 0, w, w ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [120, 7, 83] Linear Code over GF(2^2) Puncturing of [1] at { 121 } last modified: 2012-08-21
Lb(120,7) = 82 is found by truncation of: Lb(126,7) = 88 BKW Ub(120,7) = 85 BK
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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