lower bound: | 122 |
upper bound: | 122 |
Construction of a linear code [186,6,122] over GF(3): [1]: [187, 6, 123] Linear Code over GF(3) Code found by Tatsuya Maruta and Yusuke Oya Construction from a stored generator matrix: [ 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 1, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 2, 0, 1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 1, 1, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1, 1, 0, 1, 2, 1, 1, 2, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 1, 2, 1, 1, 1, 0, 1, 0, 2, 1, 0, 1, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 2, 2 ] [ 0, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 2, 1, 2, 2, 1, 0, 2, 2, 1, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 1, 0, 1, 1, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 0, 1, 1, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 2, 2, 1, 2, 0, 0, 2, 0, 2, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 1, 2 ] [ 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 1, 1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 2, 2, 1, 2, 0, 1, 2, 2, 2, 2, 0, 2, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 0, 2, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 1, 2, 2, 2, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 2, 0, 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 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, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1 ] [2]: [186, 6, 122] Linear Code over GF(3) Puncturing of [1] at { 187 } last modified: 2011-06-27
Lb(186,6) = 121 is found by truncation of: Lb(191,6) = 126 BKW Ub(186,6) = 122 follows by a one-step Griesmer bound from: Ub(63,5) = 40 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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