lower bound: | 85 |
upper bound: | 90 |
Construction of a linear code [128,9,85] over GF(4): [1]: [129, 10, 85] Linear Code over GF(2^2) Code found by Dirk Hachenberger and Martin Steinbach Construction from a stored generator matrix: [ 1, 0, 0, 1, 0, 1, w, 1, 0, 0, 0, 0, 0, w, w, 0, 0, 1, w^2, w, 0, 1, w, 1, w, 0, 0, 1, 0, 0, w^2, 0, 0, w, w, 1, w, 1, 0, 0, w, w^2, w^2, 1, 0, w, 1, w^2, w, w, 0, 1, 1, w, w, 0, w^2, 1, 1, 1, 0, w, 0, 0, w, w, 0, 0, w^2, 0, 1, w, w^2, w, 0, w^2, 1, 1, 0, w^2, 0, w^2, w, w^2, w, 1, w, w, w, w, w^2, 1, w^2, w, w^2, w^2, 0, w^2, w, 0, 1, 1, 0, 0, 1, 1, w^2, w, 1, w^2, 0, w, w^2, w^2, 1, 0, 1, 0, w, 1, 0, 1, w, w^2, w, w, 1, w, 0 ] [ 0, 1, 0, 1, 0, w^2, 0, 1, w, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, w^2, w, w^2, 1, w^2, 1, 0, 0, w, 1, 1, w^2, w, w, w, w, 1, w^2, w, 1, w^2, w, 0, 0, 0, w^2, w, 0, w, 1, w^2, w, 1, 1, w, w, 0, w, w^2, w^2, w^2, 0, w, w^2, w, w^2, w^2, w, w, 0, 1, w, 1, w, w, w^2, w^2, w, w^2, 0, w, 0, 1, w, w^2, 0, w^2, 1, w, w, w, 1, 0, 1, 0, w^2, w^2, 1, 0, w^2, w, 1, w^2, 0, w^2, 0, 1, 0, 0, w, w^2, 1, 0, w^2, 0, 1, w^2, 0, 1, 0, 0, w^2, w^2, 1, w, 1, 1, w^2, 1, 0 ] [ 0, 0, 1, 1, 0, w, w, w, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, 0, w^2, 0, 1, 0, 1, w^2, w^2, w^2, 1, 0, 1, 0, 0, w, w, w, w^2, 0, w, w^2, 0, 1, 1, 0, w, 0, 1, w^2, 1, 0, w^2, w, w, w, w, w, w^2, 1, 1, 1, w^2, w, 1, 1, w, w, 1, 0, 1, w, 0, 1, w^2, w, 1, w^2, 0, w, 0, w^2, w, 0, w, 1, w^2, 1, 0, w, w, w, 0, 1, w, w, 0, 0, 1, 0, w, 1, w^2, 1, w^2, w, 0, w^2, 0, w^2, w, 0, 1, w^2, 1, 0, w^2, 1, w^2, w, 1, 0, w, 1, 0, 1, w^2, 0, 1, 1, w ] [ 0, 0, 0, 0, 1, 1, 1, w^2, w, 0, 0, 0, 0, 0, 0, 0, 0, w, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 1, 1, w^2, w^2, 0, 0, 0, 0, w^2, w^2, 1, 1, w, w, 0, 0, 1, 1, w^2, w^2, 1, 1, w, w, 0, 0, 0, 0, w^2, w^2, 0, 0, 1, 1, w, w, w, w, w, w, w^2, w^2, 1, 1, 1, 1, w, w, w, w, 1, 1, w^2, w^2, 1, 1, 1, 1, w^2, w^2, 0, 0, 1, 1, w, w, 1, 1, w^2, w^2, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w^2, w^2, w^2, w^2, 1, 1, w, w, 1, 1, w, w, 1, 1, w^2, w^2, 1, 1, w^2, w^2, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, 0, 0, w, w, 1, 1, w, w^2, 0, w, 1, 0, w^2, w^2, 1, 0, 1, w^2, 1, w^2, w, 0, w^2, w, 0, 1, w^2, w^2, w, 0, w, w^2, 0, 1, 0, w, w, 1, 1, w, w, 0, 1, 1, 1, w^2, 1, w^2, 0, w^2, w, 0, 0, 0, 0, 1, w^2, 1, w, 0, w^2, 0, w^2, w, 1, 1, w^2, 1, w^2, w, 0, w, 1, w^2, w, w^2, w, 0, w^2, w, w, w, 1, w^2, 0, 0, w, w, w, w^2, w, w, 1, 1, w, w^2, w^2, w^2, 1, w^2, 0, 1, 0, 1, 0, 1, 0, 1, 0, w, w, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, w^2, 1, 0, 0, w, w, 1, 1, w^2, w, w, 0, 0, 1, w^2, w^2, 0, 1, w^2, 1, w^2, 1, 0, w, w, w^2, 1, 0, w^2, w^2, 0, w, w^2, w, 1, 0, w, 0, 1, w, w, 1, 0, w, 1, 1, w^2, 1, w^2, 1, w^2, 0, 0, w, 0, 0, 1, 0, 1, w^2, 0, w, 0, w^2, w, w^2, 1, 1, 1, w^2, w, w^2, w, 0, w^2, 1, w^2, w, 0, w, w, w^2, w, w, w^2, 1, 0, 0, w, w, w^2, w, w, w, 1, 1, w^2, w, w^2, w^2, w^2, 1, 1, 0, 1, 0, 1, 0, 1, 0, w, 0, w^2, w, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, 0, 0, w^2, 1, 0, w^2, 0, 1, w, w^2, w, 0, 0, w^2, w^2, 0, w, 0, w, 1, 1, 1, w^2, w, w, w^2, 1, 1, 0, 1, 0, w, 0, 1, w, 1, w^2, 1, w^2, 1, w^2, w^2, w^2, 1, 1, 1, w, w^2, w^2, w^2, 0, 1, 0, w^2, w, 1, 1, 1, w^2, 1, 1, 1, 0, w^2, w, 0, w, 1, w, 1, 1, w^2, 0, w, w^2, w^2, w, w, 1, 0, w, 1, w^2, 0, w^2, w^2, w^2, w, w^2, 0, w, 0, w^2, w, w, w, w, w^2, 1, w^2, w, w^2, w^2, 0, 1, w^2, w, 0, w, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w^2, 0, 0, 1, w^2, w^2, 0, 1, 0, w^2, w, 0, w, w^2, 0, 0, w^2, 0, w, 1, w, 1, 1, w, w^2, w^2, w, 1, 1, 1, 0, w, 0, 1, 0, 1, w, 1, w^2, 1, w^2, w^2, w^2, 1, w^2, 1, 1, w^2, w, w^2, w^2, 1, 0, w^2, 0, 1, w, 1, 1, 1, w^2, 1, 1, w^2, 0, 0, w, 1, w, 1, w, w^2, 1, w, 0, w^2, w^2, w, w, 0, 1, 1, w, 0, w^2, w^2, w^2, w, w^2, 0, w^2, 0, w, w, w^2, w, w, w^2, w, w^2, 1, w^2, w, 0, w^2, w^2, 1, 0, w, 0, w, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, 0, 1, 1, 1, 1, w, w, w^2, 1, w, 0, 1, 0, w^2, w, 0, w^2, 1, 1, w, 0, w^2, w, 1, 1, w^2, 1, 0, w^2, 1, 0, w^2, w, 0, 1, w^2, w, 0, 0, 0, 0, 1, 0, w, w, 1, w, 1, w, 1, w, w^2, w^2, w^2, 1, 0, 0, w^2, 0, w, 0, w, 0, w^2, w^2, 0, w, w^2, 1, w, 0, w^2, w, w^2, w^2, w^2, w, w^2, w^2, 1, w^2, 0, 0, w, 1, w, 0, w, w^2, 1, 1, w, w, w, 1, 1, w, 0, 0, w, 1, w^2, 1, w^2, w, w, w, w, w, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w^2, 1, 0, 1, 1, w, 1, w^2, w, w, 1, 1, 0, w^2, 0, 0, w, 1, w^2, w, 1, w^2, 0, 1, w, w^2, 1, 0, 1, 1, w^2, w^2, 0, 0, w, w^2, 1, 0, w, 0, 0, 1, 0, w, 0, 1, w, 1, w, 1, w, w^2, w, w^2, w^2, 0, 1, w^2, 0, w, 0, w, 0, w^2, 0, 0, w^2, w^2, w, w, 1, w^2, 0, w^2, w, w^2, w^2, w^2, w, 1, w^2, 0, w^2, w, 0, w, 1, w, 0, 1, w^2, w, 1, w, w, 1, 1, 0, w, w, 0, w^2, 1, w^2, 1, w, w, w, w, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [128, 9, 85] Linear Code over GF(2^2) Shortening of [1] at { 129 } last modified: 2016-03-30
Lb(128,9) = 83 is found by truncation of: Lb(133,9) = 88 DaH Ub(128,9) = 90 is found by considering shortening to: Ub(126,7) = 90 is found by considering truncation to: Ub(124,7) = 88 LP
LP: Follows from the linear programming bound.
Notes
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