lower bound: | 53 |
upper bound: | 56 |
Construction of a linear code [93,10,53] over GF(3): [1]: [95, 11, 54] Linear Code over GF(3) code found by Tatsuya Maruta Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 1, 0, 2, 2, 0, 1, 0, 1, 0, 2, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 1, 0, 2, 2, 0, 1, 0, 1, 1, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 0, 0, 1, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 2, 1, 1, 0, 2, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 0, 1, 0, 0, 2, 1, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 0, 1, 2, 0, 1, 0, 1, 0, 2, 2, 0, 2, 1 ] [2]: [94, 10, 54] Linear Code over GF(3) Shortening of [1] at { 95 } [3]: [93, 10, 53] Linear Code over GF(3) Puncturing of [2] at { 94 } last modified: 2006-10-04
Lb(93,10) = 53 is found by shortening of: Lb(94,11) = 53 is found by truncation of: Lb(95,11) = 54 MST Ub(93,10) = 56 follows by a one-step Griesmer bound from: Ub(36,9) = 18 follows by a one-step Griesmer bound from: Ub(17,8) = 6 is found by considering shortening to: Ub(16,7) = 6 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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