lower bound: | 62 |
upper bound: | 62 |
Construction of a linear code [80,4,62] over GF(5): [1]: [83, 4, 65] Linear Code over GF(5) Construction from a stored generator matrix: [ 1, 0, 1, 0, 1, 2, 0, 3, 4, 1, 1, 2, 3, 4, 2, 3, 4, 0, 1, 3, 4, 0, 1, 4, 0, 2, 2, 4, 0, 3, 1, 2, 0, 1, 3, 3, 0, 3, 1, 2, 0, 1, 3, 4, 2, 0, 1, 4, 3, 1, 3, 0, 3, 4, 0, 1, 4, 2, 3, 1, 2, 4, 3, 1, 0, 2, 3, 1, 2, 4, 0, 3, 0, 1, 2, 0, 1, 3, 3, 0, 4, 1, 2 ] [ 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 0, 0, 0, 1, 1, 2, 3, 3, 4, 4, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4 ] [ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ] [2]: [80, 4, 62] Linear Code over GF(5) Puncturing of [1] at { 81 .. 83 } last modified: 2001-12-17
Lb(80,4) = 62 is found by truncation of: Lb(83,4) = 65 Bo2 Ub(80,4) = 62 follows by a one-step Griesmer bound from: 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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