lower bound: | 124 |
upper bound: | 124 |
Construction of a linear code [189,6,124] over GF(3): [1]: [191, 6, 126] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 0, 1, 2, 0, 1, 2, 2, 2, 0, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 0, 0, 2, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 1, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 1, 0, 2, 1, 2, 2, 1, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 0, 1, 2, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 0, 2, 0, 2, 0, 2, 1, 2, 1, 1, 2, 2, 0, 0, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 2, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 2, 0, 0, 1, 2, 0, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 0, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 0, 0, 2, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 2, 0, 1, 2, 2, 1, 2, 0, 2, 0, 1, 2, 2, 1, 1, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1 ] [2]: [189, 6, 124] Linear Code over GF(3) Puncturing of [1] at { 190 .. 191 } last modified: 2005-04-07
Lb(189,6) = 124 is found by truncation of: Lb(191,6) = 126 BKW Ub(189,6) = 124 follows by a one-step Griesmer bound from: Ub(64,5) = 41 follows by a one-step Griesmer bound from: Ub(22,4) = 13 is found by considering truncation to: 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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