lower bound: | 71 |
upper bound: | 71 |
Construction of a linear code [111,7,71] over GF(3): [1]: [112, 7, 72] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1 ] [ 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 1, 2, 0, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 1, 1, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 2, 2, 2, 1, 2, 1, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 1, 2, 0, 0, 0, 2, 1 ] [ 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 0, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 1, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 2, 2, 0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 1, 1, 2, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 2, 1, 2, 2, 0, 2, 1, 0, 2, 2, 0, 2, 1, 0, 2, 1, 1, 1, 2, 2, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 1, 2, 2, 2, 1, 1, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 0, 2, 1, 1, 0, 0, 2, 0, 1, 1, 1, 2, 1, 1 ] [2]: [111, 7, 71] Linear Code over GF(3) Puncturing of [1] at { 112 } last modified: 2001-12-17
Lb(111,7) = 71 is found by truncation of: Lb(112,7) = 72 EB1 Ub(111,7) = 71 follows by a one-step Griesmer bound from: Ub(39,6) = 23 is found by considering truncation to: Ub(37,6) = 21 Bou
EB1: Y. Edel & J. Bierbrauer, Some codes related to BCH codes of low dimension, preprint, 1995.
Notes
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