lower bound: | 91 |
upper bound: | 99 |
Construction of a linear code [159,11,91] over GF(3): [1]: [161, 11, 93] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 1, 2, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 1, 0, 1, 0, 2, 0, 1, 2, 2, 1, 1, 1, 2, 0, 2, 2, 0, 1, 0, 0, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 0, 1, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 2, 1, 0, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 0, 2, 1, 0, 1, 1, 2, 1, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 2, 1, 0, 2, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 1, 0, 2, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 0, 2, 1, 2, 2, 0, 1, 1, 2, 0, 1, 1, 0, 0, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 2, 1, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 1, 1, 1, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 1, 1, 0, 2, 2, 0, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 1, 0, 0, 1, 2, 2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 1, 0, 2, 1, 0, 1, 0, 1, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 1, 2, 1, 2, 1, 1, 1, 0, 1, 0, 2, 1, 1, 2, 2, 0, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0, 1, 2, 1, 2, 1, 2, 1, 0, 0, 0, 0, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 1, 2, 0, 2, 2, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 2, 2, 0, 1, 2, 1, 2, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 1, 1, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2, 1, 0, 2, 0, 2, 1, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 1, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 1, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 1, 1, 2, 0, 1, 1, 0, 2, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 1, 2, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 2, 1, 2, 1, 0, 2, 0, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 0, 1, 2, 1, 1, 2, 2, 0, 1, 0, 2, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2, 1, 0, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0, 2, 2, 2, 1, 2, 2, 2, 0, 1, 1, 2, 1, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 0, 1, 2, 0, 2, 2, 2, 1, 0, 2, 1, 1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 1, 1, 0, 2, 1, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 2, 1, 0, 0, 1, 1, 2, 1, 2, 2, 2, 1, 0, 1, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 2, 0, 2, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 2, 0, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 2, 2, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 1, 2, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 1, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 1, 1, 2, 1, 0, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 0, 1, 1, 0, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 1, 0, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 0, 0, 1, 2, 1, 2, 2, 0, 1, 0, 0, 2, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 1, 1, 1, 2, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 1, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 1, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 2, 1, 2, 0, 0, 1, 1, 1, 2, 0, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 1, 1, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 0 ] [2]: [159, 11, 91] Linear Code over GF(3) Puncturing of [1] at { 160 .. 161 } last modified: 2009-06-05
Lb(159,11) = 90 is found by shortening of: Lb(160,12) = 90 ARS Ub(159,11) = 99 follows by a one-step Griesmer bound from: Ub(59,10) = 33 follows by a one-step Griesmer bound from: Ub(25,9) = 11 is found by considering shortening to: Ub(24,8) = 11 BS
BS:
Notes
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