lower bound: | 58 |
upper bound: | 60 |
Construction of a linear code [80,6,58] over GF(5): [1]: [82, 6, 60] Linear Code over GF(5) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 4, 4, 0, 0, 3, 3, 1, 2, 0, 1, 1, 2, 4, 0, 3, 1, 0, 4, 3, 0, 0, 3, 1, 1, 4, 3, 2, 4, 3, 3, 2, 2, 0, 4, 3, 0, 0, 3, 2, 0, 3, 4, 1, 0, 0, 1, 1, 3, 4, 0, 1, 2, 1, 2, 1, 1, 0, 2, 3, 3, 0, 1, 4, 0, 3, 1, 3, 0, 1, 2, 0, 2, 4, 3, 3, 3, 3, 3 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 4, 2, 2, 3, 3, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 4, 4, 2, 2, 3, 3, 2, 2, 3, 3, 1, 1, 4, 4, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 4, 4, 2, 2, 3, 3, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 4, 4, 2, 2, 3, 3 ] [ 0, 0, 1, 0, 4, 3, 0, 0, 0, 0, 0, 2, 4, 1, 4, 2, 0, 3, 0, 4, 3, 1, 4, 1, 2, 3, 3, 3, 3, 3, 4, 3, 0, 2, 1, 3, 4, 0, 4, 1, 3, 2, 4, 2, 1, 0, 1, 1, 1, 1, 0, 4, 3, 1, 2, 3, 4, 1, 3, 3, 3, 3, 4, 3, 0, 2, 0, 4, 1, 3, 0, 0, 0, 0, 0, 1, 2, 4, 4, 3, 2, 0 ] [ 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 4, 2, 0, 3, 4, 1, 3, 0, 1, 2, 3, 0, 1, 4, 3, 2, 1, 1, 1, 1, 4, 0, 3, 1, 0, 3, 2, 1, 1, 4, 2, 3, 0, 2, 3, 4, 2, 2, 2, 2, 1, 2, 3, 0, 3, 2, 1, 4, 1, 1, 1, 1, 4, 0, 3, 1, 1, 2, 0, 3, 0, 0, 0, 0, 4, 3, 2, 0, 4, 0, 1, 3 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 4, 3, 1, 3, 0, 2, 2, 3, 4, 0, 1, 4, 2, 3, 1, 3, 4, 0, 3, 0, 2, 1, 1, 1, 1, 1, 4, 1, 2, 3, 2, 2, 2, 2, 1, 2, 0, 3, 0, 2, 4, 3, 1, 4, 2, 3, 4, 0, 1, 3, 2, 1, 3, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 4, 1, 3, 1, 2, 3, 0, 2, 0, 3, 4 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 1, 4, 2, 0, 1, 0, 4, 3, 4, 1, 3, 2, 0, 3, 2, 1, 4, 2, 0, 1, 2, 2, 2, 2, 1, 4, 3, 2, 4, 4, 4, 4, 1, 0, 2, 4, 3, 1, 4, 0, 4, 1, 3, 2, 2, 1, 0, 3, 0, 1, 4, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 0, 3, 1, 0, 4, 2, 1, 3, 0, 4 ] [2]: [80, 6, 58] Linear Code over GF(5) Puncturing of [1] at { 81 .. 82 } last modified: 2008-08-08
Lb(80,6) = 57 is found by truncation of: Lb(81,6) = 58 DG1 Ub(80,6) = 60 follows by a one-step Griesmer bound from: Ub(19,5) = 12 is found by considering shortening to: Ub(17,3) = 12 Hi4
Hi4: R. Hill, Optimal linear codes, pp. 75-104 in: Cryptography and Coding II (C. Mitchell, ed.), Oxford Univ. Press, 1992.
Notes
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