lower bound: | 57 |
upper bound: | 63 |
Construction of a linear code [105,11,57] over GF(3): [1]: [103, 11, 57] 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, 1, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 2, 1, 0, 0, 2, 2, 2, 0, 1, 2, 0, 0, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 1, 0, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0, 1, 1, 2, 1, 0, 2, 2, 1, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 1, 0, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 2, 1, 1, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 2, 1, 1, 2, 0, 1, 0, 0, 0, 1, 2, 2, 2, 0, 1, 0, 2, 2, 2, 1, 1, 0, 2, 1, 1, 1, 0, 1, 2, 0, 0, 1, 2, 1, 1, 1, 2, 0, 2, 2, 1, 1, 2, 1, 0, 1, 2, 0, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 0, 1, 1, 0, 1, 1, 1, 2, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 0, 1, 2, 1, 2, 2, 1, 2, 0, 1, 1, 1, 0, 0, 1, 1, 2, 2, 2, 1, 0, 1, 0, 1, 2, 2, 1, 2, 1, 1, 1, 0, 0, 1, 2, 0, 2, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 2, 1, 0, 1, 2, 2, 2, 1, 2, 2, 1, 0, 0, 0, 1, 0, 1, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 1, 2, 1, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 2, 0, 1, 1, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 2, 2, 1, 2, 2, 2, 0, 1, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 1, 1, 0, 2, 2, 0, 1, 0, 0, 1, 1, 2, 1, 2, 2, 1, 0, 0, 1, 2, 2, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 1, 2, 1, 2, 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 0, 1, 0, 2, 1, 1, 0, 1, 2, 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 2, 1, 0, 2, 2, 2, 0, 2, 1, 2, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 1, 0, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 2, 0, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 2, 0, 2, 1, 1, 2, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 2, 1, 0, 1, 0, 2, 2, 2, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 1, 0, 1, 2, 1, 0, 2, 1, 2, 1, 0, 0, 2, 2, 2, 2, 2, 1, 1, 2, 1 ] [2]: [105, 11, 57] Linear Code over GF(3) ExtendCode [1] by 2 last modified: 2009-06-05
Lb(105,11) = 56 is found by lengthening of: Lb(102,11) = 56 MST Ub(105,11) = 63 follows by a one-step Griesmer bound from: Ub(41,10) = 21 follows by a one-step Griesmer bound from: Ub(19,9) = 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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