lower bound: | 121 |
upper bound: | 123 |
Construction of a linear code [189,7,121] over GF(3): [1]: [188, 7, 121] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 2, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 0, 0, 2, 1, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0, 2, 1, 2, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 2, 1, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2, 2, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 1, 2, 2, 2, 2, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 2, 1, 1, 2, 1, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 2, 1, 1 ] [2]: [189, 7, 121] Linear Code over GF(3) ExtendCode [1] by 1 last modified: 2008-12-29
Lb(189,7) = 120 is found by truncation of: Lb(192,7) = 123 GO Ub(189,7) = 123 follows by a one-step Griesmer bound from: Ub(65,6) = 41 follows by a one-step Griesmer bound from: Ub(23,5) = 13 is found by considering shortening to: 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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