lower bound: | 116 |
upper bound: | 116 |
Construction of a linear code [177,6,116] over GF(3): [1]: [178, 6, 117] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 0, 2, 2, 2, 1, 0, 2, 1, 2, 2, 0, 1, 1, 1, 2, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 1, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 0, 2, 0, 2, 1, 1, 2, 0, 1, 2, 2, 0, 0, 1, 2, 1, 1, 2, 0, 0, 2, 1, 0, 2, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 1, 2, 0, 0, 2, 0, 1, 2, 2, 1, 0, 1, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 0, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 2, 2, 0, 2, 1, 2, 2, 1, 2, 1, 2, 2, 0, 2, 1, 1, 2, 1, 2, 2, 0, 2, 2, 2, 1, 2, 0, 1, 0, 2, 1, 0, 2, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 0, 1, 2, 1, 1, 0, 2, 0, 2, 0, 1, 2, 0, 2, 1, 2, 0, 1, 1, 0, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 1, 0, 0, 0, 2, 1, 2, 2, 0, 0, 1, 1, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 0, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 0, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 1, 2, 2, 0, 1, 1, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 1, 1, 0, 2, 2, 0, 1, 2, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1, 1, 1, 2, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 2, 2, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 1, 1, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2, 2, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 1, 2, 1, 2, 0, 0, 0, 1, 1, 2, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 0, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 0, 1, 1, 2, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 0, 1, 1, 2, 2, 1, 0, 1, 2, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 2, 2, 1, 0, 1, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 2, 0, 1, 0, 1, 2, 2, 1, 0, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 0, 1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1 ] [2]: [177, 6, 116] Linear Code over GF(3) Puncturing of [1] at { 178 } last modified: 2012-03-29
Lb(177,6) = 115 is found by truncation of: Lb(179,6) = 117 Bo3 Ub(177,6) = 116 follows by a one-step Griesmer bound from: Ub(60,5) = 38 follows by a one-step Griesmer bound from: Ub(21,4) = 12 HN
HN: R. Hill & D.E. Newton, Optimal ternary linear codes, Des. Codes Cryptogr. 2 (1992), 137-157.
Notes
|