lower bound: | 114 |
upper bound: | 118 |
Construction of a linear code [183,8,114] over GF(3): [1]: [183, 8, 114] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 1, 1, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 2, 2, 2, 2, 1, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 2, 2, 2, 1, 1, 1, 2, 1, 0, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 1, 0, 0, 2, 1, 2, 0, 2, 1, 1, 2, 0, 2, 1, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0, 1, 2, 0, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 2, 1, 1, 2, 1, 1, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 0, 2, 1, 0, 2, 1, 1, 0, 2, 2, 2, 2, 2, 1, 1, 0, 2, 0, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 2, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 1, 2, 2, 1, 2, 0, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 1, 1, 2, 2, 1, 1, 0, 1, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 0, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 0, 1, 2, 1, 1, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 1, 2, 1, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 0, 1, 2, 2, 1, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 2, 1, 0, 1, 2, 2, 1, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 1, 0, 2, 1, 1, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 0, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 0, 1, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 1, 1, 2, 0, 1, 1, 0, 1, 2, 0, 2, 2, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 1, 1, 1, 2, 2, 2, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 2, 2, 0, 0, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 2, 1, 2, 0, 2, 1, 1, 1, 2, 1, 2, 1, 0, 0, 2, 1, 2, 2, 2, 1, 1, 0, 0, 0, 2, 0, 2, 2, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 0, 2, 2, 1, 2, 2, 0, 2, 1, 1, 2, 1, 2, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2, 2, 1, 0, 1, 2, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 1, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2, 2, 1, 1, 2, 1, 0, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 2, 2, 1, 2, 2, 1, 0, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 2, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 1, 1, 2, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 0, 2, 2, 1, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 2, 2, 2, 1, 0, 1, 1, 1, 0, 0, 0, 0, 2, 1, 1, 2, 1, 1, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 0, 2, 2, 1, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 0, 2, 1, 2, 2, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 1, 1, 0, 0, 0, 2, 1, 0, 1, 2, 2, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 0, 1, 2, 2, 2, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 2, 2, 0, 1, 2, 0 ] last modified: 2008-11-04
Lb(183,8) = 113 is found by truncation of: Lb(184,8) = 114 GO2 Ub(183,8) = 118 follows by a one-step Griesmer bound from: Ub(64,7) = 39 follows by a one-step Griesmer bound from: Ub(24,6) = 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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