lower bound: | 116 |
upper bound: | 120 |
Construction of a linear code [186,8,116] over GF(3): [1]: [187, 8, 117] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 1, 1, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1, 1, 2, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 1, 1, 0, 2, 2, 1 ] [ 0, 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, 2, 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, 1, 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, 2, 1, 0, 0, 2, 1, 2, 0, 2, 1, 1, 2, 0, 2, 1, 1, 0 ] [ 0, 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, 2, 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, 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, 2, 1, 0, 1, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 0, 0, 1 ] [ 0, 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, 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, 2, 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, 0, 2, 1, 2, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 0, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 2, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 2, 1, 2, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 1, 1, 2, 1, 1, 2, 2, 0, 2, 2, 1, 0, 0, 2 ] [ 0, 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, 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, 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, 1, 0, 2, 0, 2, 2, 2, 1, 2, 2, 1, 0, 1, 2, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 1, 0, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 2, 0, 1, 2, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 0, 2, 1, 1, 2, 2, 0, 1, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 1, 1, 2, 1, 2, 0, 0, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 0, 2, 2, 0, 0, 2, 2, 1, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] [2]: [186, 8, 116] Linear Code over GF(3) Puncturing of [1] at { 187 } last modified: 2008-11-04
Lb(186,8) = 114 is found by truncation of: Lb(192,8) = 120 GO2 Ub(186,8) = 120 follows by a one-step Griesmer bound from: Ub(65,7) = 40 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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