lower bound: | 107 |
upper bound: | 110 |
Construction of a linear code [171,8,107] over GF(3): [1]: [172, 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, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 0, 0, 1, 1, 2, 1, 1, 2, 2, 1, 2, 0, 0, 2, 2, 0, 2, 1, 1, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 0, 2, 2, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 1, 2, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 1, 1, 2, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 1, 2, 0, 2, 0, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 2, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 0, 2, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 1, 2, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 1, 0, 2, 0, 2, 0, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 1, 2, 2, 1, 1, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 2, 0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 2, 0, 2, 2, 1, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 0, 2, 1, 2, 0, 1, 2, 0, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 0, 1, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 2, 0, 1, 0, 0, 2, 1, 2, 1, 0, 2, 1, 0, 1, 0, 2, 1, 1, 2, 0, 0, 0, 1, 1, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2, 2, 1, 1, 0, 1, 0, 2, 0, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 0, 1, 1, 0, 1, 0, 1, 2, 1, 0, 2, 1, 2, 2, 2, 1, 2, 2, 0, 2, 1, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 0, 2, 2, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 1, 1, 0, 0, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 1, 1, 0, 1, 0, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 2, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 2, 2, 1, 1, 2, 1, 1, 0, 2, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 0, 2, 2, 1, 1, 2, 2, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 1, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 2, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 1, 0, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 0, 2, 2, 2, 1, 0, 1, 1, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 0, 2, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 2, 2, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 0, 2, 2, 1, 2, 0, 0, 2, 1, 2, 0, 1, 2, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 1, 2, 2, 0, 1, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 1, 2, 2, 1, 0, 2, 2, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 0, 2, 1, 2, 0, 0, 2, 1, 0, 1, 2, 1, 1, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 1, 2, 1, 2, 2, 2, 2, 1, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 1, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 1, 0, 2, 1, 2, 2, 1, 0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 1, 0, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 1, 2, 2, 1, 0, 0, 2, 2, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 1, 2, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 2, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 2, 2, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1 ] [2]: [171, 8, 107] Linear Code over GF(3) Puncturing of [1] at { 172 } last modified: 2008-11-06
Lb(171,8) = 106 is found by truncation of: Lb(173,8) = 108 Koh Ub(171,8) = 110 follows by a one-step Griesmer bound from: Ub(60,7) = 36 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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