lower bound: | 7 |
upper bound: | 7 |
Construction of a linear code [16,8,7] over GF(4): [1]: [18, 9, 8] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 0, w, w^2, w, 1, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, 0, w, 0, w, w, w^2, w^2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, w^2, 1, 0, 1, w^2, w, 1, w, w^2, w ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, 1, w, w, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, w^2, w^2, 1, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, w^2, 0, 1, 1, 0, w, 1, w, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, 0, 1, 0, w^2, w^2, 0, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, w^2, 1, 0, 0, 1, w^2, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, w^2, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [17, 9, 7] Linear Code over GF(2^2) Puncturing of [1] at { 18 } [3]: [16, 8, 7] Linear Code over GF(2^2) Shortening of [2] at { 17 } last modified: 2001-12-17
Lb(16,8) = 7 is found by shortening of: Lb(17,9) = 7 is found by truncation of: Lb(18,9) = 8 MOS Ub(16,8) = 7 is found by considering shortening to: Ub(11,3) = 7 is found by considering truncation to: Ub(10,3) = 6 GH
MOS: F.J. MacWilliams, A.M. Odlyzko, N.J.A. Sloane & H.N. Ward, Self-dual codes over GF(4), J. Comb. Th. (A) 25 (1978) 288-318.
Notes
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