lower bound: | 108 |
upper bound: | 112 |
Construction of a linear code [174,8,108] over GF(3): [1]: [173, 8, 108] Linear Code over GF(3) code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 2, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 1, 1, 2, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 2, 1, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 0, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 2, 1, 0, 2, 1, 0, 1, 2, 2, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 1, 0, 2, 0, 1, 1, 2, 2, 1, 1, 2, 0, 2, 2, 0, 1, 1, 1, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 0, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 1, 1, 2, 1, 0, 0, 2, 1, 1, 1, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 1, 2, 2, 1, 0, 1, 0, 1, 2, 2, 1, 0, 1, 0, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 1, 1, 0, 0, 1, 0, 2, 1, 2, 0, 1, 1, 2, 2, 1, 2, 2, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 2, 2, 0, 2, 1, 2, 1, 2, 2, 2, 1, 0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 1, 0, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 0, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 1, 2, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 0, 0, 2, 2, 1, 2, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 2, 1, 2, 2, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 2, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 1, 1, 2, 2, 0, 2, 1, 2, 1, 1, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 0, 2, 2, 0, 2, 1, 0, 1, 2, 2, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2, 1, 2, 1, 1, 0, 0, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 1, 1, 0, 2, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 2, 0, 1, 2, 2, 2, 0, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 0, 0, 0, 2, 1, 1, 0, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 2, 2, 1, 1, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 0, 1, 2, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 2, 1, 2, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 1, 0, 2, 0, 1, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 1, 2, 0, 0, 2, 2, 1, 1, 2, 2, 2, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 1, 1, 1 ] [ 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0 ] [2]: [174, 8, 108] Linear Code over GF(3) ExtendCode [1] by 1 last modified: 2006-02-21
Lb(174,8) = 108 is found by lengthening of: Lb(173,8) = 108 Koh Ub(174,8) = 112 follows by a one-step Griesmer bound from: Ub(61,7) = 37 follows by a one-step Griesmer bound from: Ub(23,6) = 12 is found by considering shortening to: Ub(21,4) = 12 HN
Koh: Axel Kohnert, email, 2006.
Notes
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