lower bound: | 80 |
upper bound: | 80 |
Construction of a linear code [123,6,80] over GF(3): [1]: [124, 6, 81] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 2, 0, 1, 2, 2, 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 1, 2, 0, 0, 2, 2, 1, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 1, 1, 1, 2, 1, 1, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0 ] [ 0, 1, 0, 2, 0, 0, 1, 2, 1, 2, 1, 1, 2, 0, 0, 2, 0, 2, 1, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 2, 0, 1, 0, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 2, 2, 2, 1, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 2, 0, 2, 1, 1, 0, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 2, 2, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 0, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2 ] [ 0, 0, 1, 2, 1, 0, 2, 1, 2, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 1, 1, 0, 2, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0, 2, 1, 1, 0, 2, 0, 1, 2, 1, 1, 0, 2, 2, 0, 0, 1, 2, 0, 2, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 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, 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, 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 ] [ 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 ] [2]: [123, 6, 80] Linear Code over GF(3) Puncturing of [1] at { 124 } last modified: 2001-12-17
Lb(123,6) = 80 is found by truncation of: Lb(124,6) = 81 Bo1 Ub(123,6) = 80 follows by a one-step Griesmer bound from: Ub(42,5) = 26 is found by considering truncation to: Ub(40,5) = 24 vE1
vE1: M. van Eupen, Some new results for ternary linear codes of dimension $5$ and $6$, IEEE Trans. Inform. Theory 41 (1995) 2048-2051.
Notes
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