lower bound: | 108 |
upper bound: | 113 |
Construction of a linear code [160,9,108] over GF(4): [1]: [162, 9, 110] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, 0, w^2, 0, 1, w^2, w^2, w, 0, 1, w, 1, 0, 0, w, w^2, 0, 1, 1, 0, 1, w, 1, w, w^2, 1, 1, 0, 1, w, w, 1, 0, 1, 0, 0, 0, 1, w^2, 0, w^2, w^2, w^2, 0, w, 0, 0, w^2, 0, w, w^2, w, 1, 1, w^2, w^2, 1, w^2, w, w^2, 0, 1, w^2, 0, 1, w^2, w^2, w, w, w, 1, w^2, 0, 1, w, 1, 1, 0, w, w, 1, 0, w^2, w, 1, 1, 1, w^2, w^2, w, 0, 0, w^2, w, 0, w^2, 1, w^2, w, w^2, w, w, 1, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w^2, w^2, 0, w^2, 0, 0, 0, w, 0, w, 1, 1, w, 0, w, w, w, w^2, 1, w, 1, w, w, w, 0, w^2, 1, 0, 0, w, 1, w, w, 0, 1, w^2, w^2, w, 0, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, 0, w^2, 0, 1, w^2, w^2, w, 1, 1, w, 1, 0, 0, w, w^2, 0, 1, 1, 0, 1, w, 1, w, w^2, 1, 1, 0, 1, w, w, 1, 0, 1, 0, 0, 0, 1, w^2, 0, w^2, w^2, w^2, 0, w^2, 0, 0, w^2, 0, w, w^2, w, 1, 1, w^2, w^2, 1, w^2, w, w^2, 0, 1, 0, 0, 1, w^2, w^2, w, w, w, 1, w^2, 0, 1, w, 1, 1, 0, w, w, w, 0, w^2, w, 1, 1, 1, w^2, w^2, w, 0, 0, w^2, w, 0, w^2, 1, w^2, w^2, w^2, w, w, 1, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w^2, w^2, 0, w, 0, 0, 0, w, 0, w, 1, 1, w, 0, w, w, w, w^2, 1, w, 1, 0, w, w, 0, w^2, 1, 0, 0, w, 1, w, w, 0, 1, w^2, w^2, w, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, w^2, w, 1, w^2, 1, w^2, 0, w, 1, w, w^2, w, w, 1, 1, 0, w, 0, 0, w, w^2, w, 1, 0, w, w^2, w^2, w, 0, 0, 1, 0, 1, w^2, 1, 0, w^2, 0, w^2, 1, w, w^2, w^2, 0, 1, w^2, 0, w, w^2, w, w, w, 0, w^2, 0, w, w, w^2, w^2, 1, w^2, w, 1, 1, 0, w^2, 1, 1, w, w, 0, w^2, 1, w^2, w, w^2, 1, 1, w, w, w^2, 0, w, w, 1, w^2, w, w^2, w, w^2, 1, 1, 0, w^2, 1, 1, 1, w^2, 1, 0, w^2, w, 0, w^2, w^2, 1, w^2, w, w^2, 0, w^2, 0, w^2, w, 0, w, 0, 0, 1, w^2, w^2, 1, 0, w, 0, 1, w^2, 1, 0, 0, 0, w, w, 1, 1, w^2, 1, w, 1, 0, w^2, w, w^2, w^2, w, 1, w^2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, w^2, w, 1, w^2, 1, w^2, 0, w, 1, w, w^2, w, w, 1, 1, 0, w, 0, 0, w, w^2, 0, 1, 0, w, w^2, w^2, w, 0, 0, 1, 0, 1, w^2, 1, 0, w^2, 0, w^2, w^2, w, w^2, w^2, 0, 1, w^2, 0, w, w^2, w, w, w, 0, w^2, 0, w, w, 1, w^2, 1, w^2, w, 1, 1, 0, w^2, 1, 1, w, w, 0, w^2, 1, w^2, w, 0, 1, 1, w, w, w^2, 0, w, w, 1, w^2, w, w^2, w, w^2, 1, 1, 0, 0, 1, 1, 1, w^2, 1, 0, w^2, w, 0, w^2, w^2, 1, w^2, w, w^2, 0, w^2, w, w^2, w, 0, w, 0, 0, 1, w^2, w^2, 1, 0, w, 0, 1, w^2, 1, 0, 1, 0, w, w, 1, 1, w^2, 1, w, 1, 0, w^2, w, w^2, w^2, w, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, w, 0, w, 1, w^2, 0, w, 1, 0, w^2, w^2, 0, 1, 0, w, 1, 0, w, w^2, w, w, 1, 1, w, 0, w, w, w, w^2, 0, w^2, 1, w, 0, 0, w^2, 1, 1, w, 0, 1, w^2, w^2, 1, w^2, w^2, w^2, 0, 1, w, 1, w, w^2, w, 0, w^2, 1, 1, w^2, w, w^2, w^2, w^2, w, 0, 0, 1, w, w^2, 1, w^2, w^2, w, 0, 0, 0, 0, w, 1, w^2, 1, w, w^2, 0, 0, w, 1, 1, w, 1, w, 1, w^2, w^2, 1, 0, w, w, w^2, w, w^2, 0, 1, 1, 1, w^2, w, 1, 1, w^2, 0, w, w^2, w^2, 1, 0, w, w^2, 1, 0, 1, w, w, w, w^2, 0, w, w^2, w^2, w, w, 1, w, w^2, w, 0, w^2, 0, 1, 1, 0, w^2, 1, w, 0, 1, w^2, w, 0, w, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 1, w^2, w, 1, 1, w, 1, 0, w, w^2, 1, w^2, w^2, w, w, 0, w^2, 0, 0, w^2, 1, w^2, 0, w, 0, w^2, 1, w^2, 0, 0, w, 0, w, 1, w, 0, 1, 0, 1, w, 1, w^2, 1, 1, w, 1, 0, w^2, 1, w^2, w^2, w^2, 0, 1, 0, w^2, w^2, 1, w, 1, w, 1, w, w, 0, 1, w, w, w^2, w^2, 0, 1, w, 1, w^2, 1, 0, w, w, w^2, 1, 0, w^2, w^2, w, 1, w^2, 1, w^2, 1, w, w, 0, 1, 0, w, w, w, w, 0, 1, w^2, 0, 1, 1, w, 1, w^2, 1, 0, 1, 0, w^2, 1, w^2, 0, 0, 0, w, 1, 1, w, 0, w^2, 0, w, 1, w, 0, 0, w, 0, w^2, w^2, w, 1, w, w^2, w, 0, 1, w^2, 1, 1, w^2, w, 1, w, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 1, w^2, w, 1, 1, w, 1, w^2, w, w^2, 1, w^2, w^2, w, w, 0, w^2, 0, 0, w^2, 1, w^2, 0, w, 0, 1, 1, w^2, 0, 0, w, 0, w, 1, w, 0, 1, 0, 1, w, 1, w^2, 1, 0, w, 1, 0, w^2, 1, w^2, w^2, w^2, 0, 1, 0, w^2, w^2, 1, w, 1, w, w^2, w, w, 0, 1, w, w, w^2, w^2, 0, 1, w, 1, w^2, 1, 0, w, w, w^2, 1, 0, w^2, w^2, w, 1, w^2, 1, w^2, 1, w, w, 0, 1, 0, w, w, 1, w, 0, 1, w^2, 0, 1, 1, w, 1, w^2, 1, 0, 1, 0, w^2, 1, w^2, w^2, 0, 0, w, 1, 1, w, 0, w^2, 0, w, 1, w, 0, 0, w, 0, w^2, w, w, 1, w, w^2, w, 0, 1, w^2, 1, 1, w^2, w, 1, w, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, w, 1, 1, w^2, 0, w, w, w, 0, 0, w^2, 1, 0, w, w, 0, w, w^2, w, w^2, 1, w, w, w, 0, w^2, w^2, w, 0, w, 0, 0, 0, w, 1, 0, 1, 1, 1, 0, w^2, 1, 0, 1, 0, w^2, 1, w^2, w, w, 1, 1, w, 1, w^2, 1, 0, w, 1, 0, 0, 1, 1, w^2, w^2, w^2, w, 1, 0, w, w^2, w, w, 0, w^2, w^2, w, w^2, 0, w^2, w, w, w, 1, 1, w^2, 0, 0, 1, w^2, 0, 1, w, 1, w^2, 1, 1, w^2, w, 1, w, 0, 1, 0, 0, 1, w, 0, 1, 1, 1, 0, 1, w^2, 0, 0, w^2, 0, w^2, w, w, w^2, 0, w^2, w^2, w^2, 1, w, w^2, w, w^2, 0, w^2, 0, 1, w, 0, 0, w^2, w, w^2, w^2, 0, w, 1, 1, w^2, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, w, 1, 1, w^2, 0, w, w^2, w, 0, 0, w^2, 1, 0, w, w, 0, w, w^2, w, w^2, 1, w, w, w, w, w^2, w^2, w, 0, w, 0, 0, 0, w, 1, 0, 1, 1, 1, 0, w^2, 1, 0, 1, 0, w^2, 1, w^2, w, w, 1, 1, w, 1, w^2, 1, 0, w, 1, 0, w, 1, 1, w^2, w^2, w^2, w, 1, 0, w, w^2, w, w, 0, w^2, w^2, w, w^2, 1, w^2, w, w, w, 1, 1, w^2, 0, 0, 1, w^2, 0, 1, w, 1, w^2, 1, w^2, w^2, w, 1, w, 0, 1, 0, 0, 1, w, 0, 1, 1, 1, 0, 1, w^2, 0, 0, w^2, 0, w^2, w, w, w^2, 0, w^2, w^2, w^2, 1, w, w^2, w, w^2, 0, w^2, 0, 1, w, 0, 0, w^2, w, w^2, w^2, 0, w, 1, 1, w^2, 0, 1, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [160, 9, 108] Linear Code over GF(2^2) Puncturing of [1] at { 161 .. 162 } last modified: 2002-10-21
Lb(160,9) = 108 is found by truncation of: Lb(162,9) = 110 MSY Ub(160,9) = 113 is found by considering shortening to: Ub(159,8) = 113 Da1
MSY: T. Maruta, M. Shinohara, F. Yamane, K. Tsuji, E. Takata, H. Miki & R. Fujiwara, New linear codes from cyclic or generalized cyclic codes by puncturing, to appear in Proc. 10th International Workshop on Algebraic and Combinatorial Coding Theory(ACCT-10) in Zvenigorod, Russia, 2006.
Notes
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