lower bound: | 66 |
upper bound: | 66 |
Construction of a linear code [85,4,66] over GF(5): [1]: [89, 4, 70] Linear Code over GF(5) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 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, 3, 3, 4, 4, 4, 4, 0, 1, 2, 3, 3, 3, 4, 4, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 4, 4 ] [ 0, 1, 0, 3, 2, 1, 4, 3, 2, 1, 0, 2, 0, 4, 3, 2, 1, 0, 4, 0, 3, 2, 1, 0, 4, 2, 1, 3, 2, 1, 0, 4, 3, 2, 1, 0, 3, 2, 0, 4, 3, 1, 4, 1, 0, 3, 2, 1, 0, 4, 2, 1, 0, 3, 1, 4, 4, 3, 4, 3, 2, 1, 0, 4, 2, 0, 4, 2, 0, 3, 1, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, 4, 2, 4, 0, 3, 2, 1, 3 ] [ 0, 0, 1, 3, 4, 0, 2, 3, 4, 0, 1, 4, 1, 2, 3, 4, 0, 1, 2, 0, 2, 3, 4, 0, 1, 3, 4, 2, 3, 4, 0, 1, 2, 3, 4, 0, 2, 4, 1, 2, 3, 0, 2, 0, 1, 4, 0, 1, 2, 3, 0, 1, 2, 4, 1, 3, 3, 4, 4, 0, 1, 2, 3, 4, 1, 3, 4, 1, 3, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 0, 2, 0, 4, 1, 2, 3, 1 ] [ 0, 0, 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, 1, 1, 1, 1, 1 ] [2]: [85, 4, 66] Linear Code over GF(5) Puncturing of [1] at { 86 .. 89 } last modified: 2001-12-17
Lb(85,4) = 66 is found by truncation of: Lb(89,4) = 70 BKM Ub(85,4) = 66 follows by a one-step Griesmer bound from: Ub(18,3) = 13 is found by considering truncation 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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