lower bound: | 150 |
upper bound: | 150 |
Construction of a linear code [228,6,150] 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 ] last modified: 2003-09-25
Lb(228,6) = 150 Bo3 Ub(228,6) = 150 follows by a one-step Griesmer bound from: Ub(77,5) = 50 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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