lower bound: | 117 |
upper bound: | 117 |
Construction of a linear code [180,6,117] over GF(3): [1]: [179, 6, 117] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 1, 1, 0, 0, 0, 0, 2, 2, 1, 1, 0, 2, 2, 2, 1, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 1, 2, 2, 1, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 2, 2, 1, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 0, 2, 2, 1, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 1, 0 ] [ 0, 1, 0, 1, 0, 0, 2, 1, 0, 2, 1, 2, 2, 0, 2, 1, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 1, 1, 0, 2, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 2, 1, 2, 2, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 1, 2, 1, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 1, 2, 1, 1, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 1, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 0, 1, 2, 1, 2, 1, 0, 2, 1, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 0, 0 ] [ 0, 0, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 2, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 0, 2, 0, 1, 1, 2, 2, 1, 2, 0, 1, 2, 1, 2, 0, 1, 1, 2, 1, 0, 2, 0, 1, 2, 2, 0, 2, 1, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 2, 0, 1, 0, 2, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 1, 2, 2, 0, 0, 2, 1, 2, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 0, 1, 1, 2, 1, 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, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ] [2]: [180, 6, 117] Linear Code over GF(3) PadCode [1] by 1 last modified: 2001-12-17
Lb(180,6) = 117 is found by lengthening of: Lb(179,6) = 117 Bo3 Ub(180,6) = 117 follows by a one-step Griesmer bound from: Ub(62,5) = 39 follows by a one-step Griesmer bound from: 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
|