lower bound: | 109 |
upper bound: | 109 |
Construction of a linear code [168,6,109] over GF(3): [1]: [170, 6, 111] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 1, 1, 0, 1, 2, 0, 2, 1, 1, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 1, 0, 1, 0, 1, 2, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 2, 1, 2, 2, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 0, 1, 0, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 1, 0, 1, 2, 1, 2, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 1, 1, 2, 0, 1, 0, 2, 0, 2, 1 ] [ 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 0, 2, 2, 0, 0, 2, 1, 2, 1, 0, 0, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 1, 0, 2, 1, 0, 0, 2, 2, 1, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 0, 2, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 1, 1, 0, 2, 0, 1, 0, 2, 0, 1, 2, 1, 1, 2, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 2, 0, 2, 1, 1, 0, 1 ] [ 0, 0, 0, 1, 1, 2, 0, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 1, 2, 2, 2, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 1, 0, 1, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 1, 2, 2, 2, 2, 0, 0, 1, 2, 0, 1, 1, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 2, 0, 0, 2, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, 2, 0, 1, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 1, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 0, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] [2]: [168, 6, 109] Linear Code over GF(3) Puncturing of [1] at { 169 .. 170 } last modified: 2001-12-17
Lb(168,6) = 109 is found by truncation of: Lb(170,6) = 111 Bo3 Ub(168,6) = 109 follows by a one-step Griesmer bound from: Ub(58,5) = 36 follows by a one-step Griesmer bound from: Ub(21,4) = 12 HN
HN: R. Hill & D.E. Newton, Optimal ternary linear codes, Des. Codes Cryptogr. 2 (1992), 137-157.
Notes
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