lower bound: | 30 |
upper bound: | 35 |
Construction of a linear code [63,12,30] over GF(3): [1]: [62, 12, 30] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 1, 1, 2, 0, 2, 1, 0, 0, 1, 2, 2, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 1, 1, 1, 0, 1, 2, 1, 2, 2, 2, 0, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1, 1, 2, 0, 1, 2, 0, 2, 2, 0, 1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 2, 2, 2, 1, 0, 0, 1, 2, 1, 1, 2, 0, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 0, 2, 2, 1, 0, 1, 2, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 2, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 2, 2, 1, 2, 2, 0, 0, 1, 2, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 1, 0, 1, 2, 1, 2, 0, 1, 2, 1, 1, 0, 0, 2, 1, 2, 2, 2, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 2, 2, 1, 2, 0, 0, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 2, 0, 1, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 2, 2, 1, 2, 0, 0, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 2, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 1, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 2, 1, 2, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 1, 2, 1, 0, 1, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1 ] [2]: [63, 12, 30] Linear Code over GF(3) ExtendCode [1] by 1 last modified: 2005-04-15
Lb(63,12) = 30 is found by truncation of: Lb(66,12) = 33 DaH Ub(63,12) = 35 follows by a one-step Griesmer bound from: Ub(27,11) = 11 is found by considering shortening to: Ub(24,8) = 11 BS
DaH: Rumen Daskalov & Plamen Hristov, New One-Generator Quasi-Cyclic Codes over GF(7), preprint, Oct 2001. R. Daskalov & P Hristov, New One-Generator Quasi-Twisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov, New Quasi-Twisted Degenerate Ternary Linear Codes, preprint, Nov 2001. Email, 2002-2003.
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