lower bound: | 72 |
upper bound: | 76 |
Construction of a linear code [108,8,72] over GF(4): [1]: [108, 8, 72] Linear Code over GF(2^2) Code found by Plamen Hristov Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, w^2, 1, 0, 1, 1, w, w, 0, w, w^2, w, 1, w^2, w, 1, 0, 0, 0, w, 0, w^2, 1, 0, 0, 1, w, w, w^2, 0, w^2, w, 1, 1, 1, w, w, 1, 1, 0, w^2, 0, w, 1, w, w^2, w^2, w^2, 0, w^2, w^2, 1, 1, 1, w^2, w, 1, 1, 0, 0, 0, w^2, 0, w^2, 0, 0, w, 1, 1, w, w^2, 0, 1, w, w^2, 0, w, 0, 1, 0, 0, 0, w, w, 1, 0, w^2, 1, 0, w, 0, w, 1, 0, w, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w^2, w, 0, 0, 0, 1, w^2, w, 0, w^2, w, 1, 0, w^2, 1, w^2, w, 1, 1, 0, 0, 1, w, w, 0, 1, 0, w^2, 0, w^2, 0, w^2, w, w, w, w, w, 0, w^2, 1, w, 1, w, w^2, 1, 1, 0, 0, 1, 1, w^2, w, 1, 0, w, 1, w^2, w, 1, w, 1, 0, 0, w, w^2, w, w^2, 0, 1, 1, w, 0, 0, w^2, w^2, 0, 0, w^2, 1, w, w^2, 1, 0, 0, 1, w^2, 1, 1, w, 0, 1, 1, w, 1, 1, 1, 1, w, w^2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, w, 0, 0, 0, 1, w^2, w, 0, w^2, w, 1, w, w^2, 1, w^2, w, 1, 1, 0, 0, 1, w, w, 0, 1, 0, w^2, 0, w^2, 0, w^2, w, w, w, w, w, 0, w^2, 1, w, 1, w, w^2, 1, 1, 0, 0, 1, 1, w^2, w, 1, 0, 0, 1, w^2, w, 1, w, 1, 0, 0, w, w^2, w, w^2, 0, 1, 1, w, 0, 0, w^2, w^2, 1, 0, w^2, 1, w, w^2, 1, 0, 0, 1, w^2, 1, 1, w, 0, 1, 1, w, 1, 1, 1, w^2, 1, w ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, w^2, 0, w^2, w, w, 1, 1, w, 0, w, w^2, w, 0, 0, w, 1, w^2, w^2, w^2, 1, 1, w^2, w^2, 0, 0, 1, w, 1, 1, 1, 0, w, w^2, w, w^2, w^2, 1, w, 0, w^2, 0, w, w^2, w^2, w, w^2, 1, w, 1, w^2, 0, 1, w^2, w, 1, 1, 0, w^2, 1, 0, 1, 1, w, 1, w, w^2, 0, w, w^2, 1, w, w, 0, w^2, w, 0, w, w, 1, w^2, w^2, 1, w^2, 0, w^2, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, w^2, w, 0, 1, 1, 0, w, w^2, 0, w, w, w^2, 1, 0, w, w, w, w, 1, w^2, w, w^2, w^2, w^2, w, 1, w, 0, w, w^2, 0, 1, 1, 0, w, 1, w, 1, 0, w, w, 1, w^2, 1, 0, 0, 1, 0, w^2, w, 1, 1, w, 0, 1, 1, w, w^2, w^2, 1, w, w, w^2, w^2, 1, w^2, 0, 0, 0, w, 0, 1, 1, w^2, 0, w, w^2, w, w, 0, w, w^2, w^2, 0, w^2, 0, 0, w^2, 0, 0, w, w^2, w, w^2, w^2, w, w, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, w^2, w, 0, 0, w^2, w^2, w^2, 1, w^2, w^2, w^2, w, 1, 0, w^2, 0, w, w, w, w, w^2, w^2, 1, w^2, w^2, 0, w, 1, 1, w, w, w^2, 0, w^2, w, 1, w, 0, w^2, 0, w^2, w, w, 1, w, 1, 1, 0, 0, w, w^2, w^2, w^2, 1, 1, w, w^2, 0, w^2, w^2, 1, w^2, w, w, w^2, 1, 0, w, w, w^2, w^2, 0, w^2, w, w, 0, 1, w^2, 0, w, 0, w, 0, 0, w, w^2, 1, w, w^2, w^2, 0, 1, 1, w, 0, 0, w, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, 1, w, 1, 1, 0, w^2, 0, w, w, 1, w, 1, w, 1, w^2, 1, 0, 0, w, w, w^2, w, 1, 0, 1, w^2, 0, 1, w^2, w^2, 1, 0, w^2, 0, w^2, 0, w^2, 0, 1, w^2, w^2, w, w^2, w^2, 1, 0, 0, w^2, w^2, 0, w, 0, 0, 0, 1, w^2, 0, 1, 0, 0, w^2, w^2, w^2, w^2, 0, w, w^2, 0, w^2, 1, w^2, 1, w^2, w^2, w, w, w, 1, 1, 0, 0, w, 0, w^2, 1, w^2, w, 1, w, w, w, w^2, 1, w, 1, w^2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, w, w^2, 1, 0, 1, 1, w, w, 0, w, w^2, 1, 1, w^2, w, 1, 0, 0, 0, w, 0, w^2, 1, 0, 0, 1, w, w, w^2, 0, w^2, w, w, 1, 1, w, w, 1, 1, 0, w^2, 0, w, 1, w, w^2, w^2, w^2, 0, w^2, w^2, 1, 1, 1, w^2, w, 1, 1, 0, 0, 0, w^2, 0, w^2, 0, 0, w, 1, 1, w, w^2, 0, 1, w, 1, 0, w, 0, 1, 0, 0, 0, w, w, 1, 0, w^2, 1, 0, w, 0, w, 1, 0, w, w^2, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-04-25
Lb(108,8) = 70 is found by truncation of: Lb(110,8) = 72 BZ Ub(108,8) = 76 follows by a one-step Griesmer bound from: Ub(31,7) = 19 is found by considering shortening to: Ub(29,5) = 19 is found by considering truncation to: Ub(26,5) = 16 BGV
BZ: E. L. Blokh & V. V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm. 10 (1974) 218-222.
Notes
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