lower bound: | 110 |
upper bound: | 114 |
Construction of a linear code [177,8,110] over GF(3): [1]: [178, 8, 111] 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, 1, 0, 0, 1, 1, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 0, 1, 2, 1, 1, 0, 1, 1, 0, 1, 2, 1, 2, 0, 2, 1, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 1, 1, 1, 0, 1, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 2, 2, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 1, 0, 1, 2, 1, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 0, 2, 2, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 0, 0, 0, 0, 2, 1, 1, 2, 1, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 1, 2, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 2, 1, 0, 1, 2, 2, 2, 1, 1, 0, 2, 1, 2, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 1, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 0, 0, 0, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 2, 2, 2, 2, 1, 0, 2, 2, 2, 0, 2, 0, 1, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 1, 0, 1, 1, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 2, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 1, 2, 0, 2, 2, 1, 1, 1, 2, 0, 0, 2, 1, 1, 1, 2, 0, 0, 2, 1, 2, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 1, 2, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 1, 2, 2, 1, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 1, 0, 2, 2, 1, 1, 2, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 1, 1, 2, 1, 0, 2, 2, 2, 0, 2, 0, 1, 2, 1, 1, 1, 2, 2, 2, 0, 1, 2, 1, 0, 2, 2, 0, 1, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 2, 2, 1, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 1, 2, 1, 1, 1, 0, 1, 0, 2, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 1, 1, 1, 2, 2, 2, 0, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 1, 1, 2, 1, 2, 2, 0, 0, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 2, 2, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 2, 0, 1, 1, 0, 0, 0, 2, 0, 1, 1, 2, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 1, 1, 0, 2, 2, 2, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 2, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 2, 0, 2, 1, 1, 1, 2, 0, 1, 2, 2, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 2, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 2, 1, 1, 0, 2, 2, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 1, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 2, 2, 0, 0, 1, 0, 2, 1, 2, 1, 0, 0, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 1, 2, 2, 0, 1, 2, 0, 1, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 1 ] [2]: [177, 8, 110] Linear Code over GF(3) Puncturing of [1] at { 178 } last modified: 2009-01-13
Lb(177,8) = 109 is found by truncation of: Lb(178,8) = 110 Koh Ub(177,8) = 114 follows by a one-step Griesmer bound from: Ub(62,7) = 38 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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