lower bound: | 75 |
upper bound: | 78 |
Construction of a linear code [123,8,75] over GF(3): [1]: [123, 8, 75] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 1, 2, 0, 0, 2, 1, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 0, 2, 0, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 1, 2, 1, 0, 2, 0, 0, 0, 1, 2, 1, 2, 0, 2, 1, 0, 1, 1, 0, 2, 2, 1, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 2, 1, 0, 0, 0, 2, 1, 0, 1, 1, 2, 2, 0, 0 ] [ 0, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 1, 2, 2, 2, 1, 2, 1, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 0, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 2, 1, 0, 1, 1, 2, 0, 2, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 2, 1, 0, 2, 0, 0, 1, 0, 2, 0, 2, 1, 0, 2, 1, 1, 1, 0, 2, 2, 2 ] [ 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 1, 1, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 1, 1, 1, 2, 0, 1, 2, 2, 2, 1, 0, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 0, 1, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2, 1, 2, 2, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 1, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2, 2, 0, 2, 0, 1, 2, 2, 1, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 1, 2, 2, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 1, 0, 1, 1, 2, 0, 0, 1, 2, 0, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 2, 2, 2, 1, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 1, 2, 0, 0, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 1, 1, 2, 2, 1, 1, 2, 1, 0, 0, 1, 2, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 1, 2, 1, 0, 2, 1, 1, 1, 2, 2, 0, 2, 1, 1, 1, 2, 0, 0, 0, 2, 2, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 1, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 0, 1, 2, 2, 1, 0, 2, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 1, 2, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 1, 1, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 1, 1, 2, 2, 2, 2, 0, 2, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 0, 2, 1, 1, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 2 ] last modified: 2009-03-02
Lb(123,8) = 74 is found by truncation of: Lb(124,8) = 75 BZ Ub(123,8) = 78 follows by a one-step Griesmer bound from: Ub(44,7) = 26 follows by a one-step Griesmer bound from: Ub(17,6) = 8 is found by considering truncation to: Ub(16,6) = 7 vE2
vE2: M. van Eupen, Four nonexistence results for ternary linear codes, IEEE Trans. Inform. Theory 41 (1995) 800-805.
Notes
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