lower bound: | 147 |
upper bound: | 148 |
Construction of a linear code [225,6,147] over GF(3): [1]: [228, 6, 150] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 2, 1, 1, 2, 1, 0, 2, 2, 1, 2, 1, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 1, 2, 2, 1, 2, 0, 1, 1, 1, 2, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 2, 0, 1, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 1, 2, 0, 0, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 1, 2, 0, 0, 2, 0, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1, 1, 2, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0, 1, 2, 0, 2, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 2, 0, 1, 1, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1, 1, 2, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 1, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 0, 1, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 0, 1, 2, 2, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1 ] [2]: [225, 6, 147] Linear Code over GF(3) Puncturing of [1] at { 226 .. 228 } last modified: 2001-12-17
Lb(225,6) = 147 is found by truncation of: Lb(228,6) = 150 Bo3 Ub(225,6) = 148 follows by a one-step Griesmer bound from: Ub(76,5) = 49 is found by considering truncation to: Ub(75,5) = 48 HN
HN: R. Hill & D.E. Newton, Optimal ternary linear codes, Des. Codes Cryptogr. 2 (1992), 137-157.
Notes
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