lower bound: | 61 |
upper bound: | 63 |
Construction of a linear code [102,8,61] over GF(3): [1]: [104, 8, 63] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 1, 0, 2, 2, 1, 2, 0, 2, 0, 0, 1, 2, 1, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 2, 2, 1, 0, 0, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 1, 1, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 1, 2, 2, 2, 1, 1, 0, 2, 0, 2, 2, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 2, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 1, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 1, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2, 1, 1, 0, 2, 1, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 1, 2, 1, 0, 0, 2, 2, 1, 1, 1, 2, 1, 0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 1, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 2, 1, 0, 2, 1, 1, 0, 0, 2, 2, 1, 0, 0, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 0, 1, 1, 1, 2, 0, 1, 2, 2, 0, 0, 2, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 0, 1, 2, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 1, 2, 0, 2, 1, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 1, 2, 1, 0, 2, 2, 2, 1, 0, 1, 2, 1, 1, 0, 2, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 1, 2, 1, 2, 0, 2, 0, 1, 1, 2, 1, 1, 2, 0, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 1, 0, 2, 2, 0, 2, 1, 2, 0, 1, 0, 1, 1, 1, 0, 2, 2, 0, 0, 1, 2, 2, 2, 0, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 0, 1, 0, 2, 2, 2, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0 ] [2]: [102, 8, 61] Linear Code over GF(3) Puncturing of [1] at { 103 .. 104 } last modified: 2008-08-08
Lb(102,8) = 60 is found by truncation of: Lb(105,8) = 63 Gu Ub(102,8) = 63 follows by a one-step Griesmer bound from: Ub(38,7) = 21 follows by a one-step Griesmer bound from: 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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