lower bound: | 124 |
upper bound: | 125 |
Construction of a linear code [192,7,124] over GF(3): [1]: [194, 7, 126] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 1, 0, 2, 1, 2, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 2, 2, 1, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 1, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 0, 1, 2, 2, 1, 2, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 1, 2, 2, 2, 2, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 1, 0, 2, 1, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 1, 1, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 2, 2, 2, 1, 1 ] [2]: [192, 7, 124] Linear Code over GF(3) Puncturing of [1] at { 193 .. 194 } last modified: 2008-12-29
Lb(192,7) = 123 GO Ub(192,7) = 125 is found by considering truncation to: Ub(191,7) = 124 Da6
GO: T. A. Gulliver & P. R. J. Östergård, Improved bounds for ternary linear codes of dimension 7, IEEE Trans. Inform. Theory 43 (1997) 1377-1381.
Notes
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