lower bound: | 88 |
upper bound: | 89 |
Construction of a linear code [138,7,88] over GF(3): [1]: [140, 7, 90] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 1, 2, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 1, 2, 1, 1, 2, 1, 1, 2, 0, 2, 1, 0, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 1, 2, 2, 2, 1, 0, 0, 1, 2, 2, 2, 1, 0, 0, 2, 0, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 0, 2, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 1, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 1, 0, 1, 0, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 1, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 2, 0, 1, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 1, 2, 1, 0, 2, 1, 1, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 2, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 2, 1, 2, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0, 1, 2, 2, 1, 1, 0, 1, 2, 2, 0, 2, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 1, 2, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2, 2, 2, 2, 1, 1, 2, 0, 2, 0, 1, 0, 1, 0, 1, 2, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 1, 2, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 2, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 1, 1, 2, 0, 1, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 1, 2, 1, 1, 0, 2, 1, 1, 2, 2, 0, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 0, 2, 1, 0, 0, 1, 0, 0, 2, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 2, 0, 2, 0, 1, 1, 2, 2, 2, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0, 1, 2, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 1, 1, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 0, 2, 0, 1, 1, 1, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 2, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 1, 0, 0, 2, 2, 2, 0, 2, 1, 0, 2, 1, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 1, 0, 1, 2, 0, 1, 1, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 2, 0, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 2, 2, 1, 1, 2, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 0, 0, 1, 0, 2, 1, 1, 0, 0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 2 ] [2]: [138, 7, 88] Linear Code over GF(3) Puncturing of [1] at { 139 .. 140 } last modified: 2005-04-15
Lb(138,7) = 87 is found by truncation of: Lb(141,7) = 90 GW2 Ub(138,7) = 89 follows by a one-step Griesmer bound from: Ub(48,6) = 29 is found by considering truncation to: Ub(47,6) = 28 HJ
HJ: R. Hill and C. Jones, The non-existence of ternary [47,6,29] codes,
Notes
|