lower bound: | 46 |
upper bound: | 46 |
Construction of a linear code [60,4,46] over GF(5): [1]: [64, 4, 50] Linear Code over GF(5) Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 0, 0, 3, 2, 0, 0, 3, 1, 0, 3, 0, 1, 0, 3, 3, 2, 0, 3, 3, 4, 0, 3, 1, 2, 0, 3, 2, 4, 0, 3, 2, 2, 3, 3, 3, 1, 3, 3, 1, 1, 3, 3, 4, 2, 3, 3, 4, 2, 3, 1, 4, 4, 3, 1, 4, 1, 3, 4, 1 ] [ 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 3, 1, 1, 0, 3, 1, 2, 0, 3, 2, 4, 0, 3, 4, 2, 0, 3, 4, 4, 0, 3, 1, 2, 3, 3, 2, 1, 3, 3, 3, 1, 3, 3, 3, 2, 3, 3, 3, 2, 3, 1, 3, 4, 3, 1, 2, 1, 3, 4 ] [ 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 2, 4, 0, 1, 4, 2, 0, 1, 4, 4, 0, 1, 1, 2, 3, 1, 2, 1, 3, 1, 3, 1, 3, 1, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 3, 2, 1, 3 ] [ 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 2, 4, 0, 1, 4, 2, 0, 1, 4, 4, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 1, 3, 2, 1 ] [2]: [60, 4, 46] Linear Code over GF(5) Puncturing of [1] at { 61 .. 64 } last modified: 2001-12-17
Lb(60,4) = 46 is found by truncation of: Lb(64,4) = 50 BKM Ub(60,4) = 46 follows by a one-step Griesmer bound from: Ub(13,3) = 9 is found by considering truncation to: Ub(12,3) = 8 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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