lower bound: | 61 |
upper bound: | 65 |
Construction of a linear code [105,9,61] over GF(3): [1]: [105, 9, 61] Linear Code over GF(3) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 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, 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, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 1, 0, 2, 2, 0, 1, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 1, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 1, 2, 1, 0, 2, 1, 2, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 0, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 1, 0, 2, 1, 1, 2, 0, 0, 2, 2, 1, 1, 2, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 2, 1, 2, 2, 2, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 2, 1, 2, 1, 1, 2, 0, 2, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 1, 0, 0, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 1, 1, 2, 0, 2, 0, 0, 1, 2, 2, 1, 1, 0, 0, 2, 0, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 1, 2, 2, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 0, 2, 1, 1, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2, 0, 1, 2, 2, 2, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 2, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 1, 0, 1, 1, 1, 2, 1, 0, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 1, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 0, 0, 0, 2, 2, 2, 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, 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, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2 ] last modified: 2007-08-31
Lb(105,9) = 60 is found by truncation of: Lb(108,9) = 63 GB1 Ub(105,9) = 65 follows by a one-step Griesmer bound from: Ub(39,8) = 21 follows by a one-step Griesmer bound from: Ub(17,7) = 7 is found by considering shortening 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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