lower bound: | 49 |
upper bound: | 54 |
Construction of a linear code [80,9,49] over GF(4): [1]: [81, 9, 50] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, w, 0, 1, w, w^2, w, 1, 1, 1, 1, w, 0, w, 0, w^2, 1, w^2, w, 1, w, 0, w^2, 0, 0, w^2, 1, w^2, 0, w^2, 1, 0, 1, 0, w, 0, 0, w^2, 1, 0, 1, w, 1, w^2, w^2, w^2, w^2, w^2, 0, w, w, w, 1, w^2, w, w^2, 1, 1, 1, w, 0, 1, w, 1, w, 0, w, 0, 1, w^2, w, w, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, w^2, w, w^2, 0, w, w, 0, 0, 0, w^2, 1, w^2, 1, 0, w, w^2, 1, 0, 1, 1, w, 0, 0, 1, w^2, 0, w, 1, 0, w^2, 0, w, w^2, 1, 1, 0, w^2, w, w, w, w^2, 1, 0, w, 0, 1, 0, w, 0, 0, w, w, 0, w^2, w^2, 0, w^2, 0, w, w^2, 1, w^2, w^2, 1, 0, 0, 1, w^2, 1, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 1, 1, w^2, w^2, 1, 0, w^2, w^2, 0, 0, w, w, w, w, 0, w, w, 0, w^2, w^2, w, w^2, 1, 1, 1, 0, 0, 1, w^2, w^2, 1, 0, 0, 0, w, w, w, w, w, w, 1, w^2, 0, w, w^2, 0, 0, w^2, w, w, 1, w, 1, 1, 1, w, 0, w^2, w, 0, 1, 1, w, w, w^2, w, 0, 0, 1, w, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, w, 0, w, w^2, w^2, 0, w^2, w^2, 1, 1, 0, 0, w, 0, w^2, 0, w^2, 0, w^2, w, w^2, w, 0, w^2, w^2, w, w, w^2, 1, 0, 0, 1, 0, w^2, w^2, 0, 1, w, w, w^2, w^2, 0, 0, 0, w, 0, w^2, w, w^2, 1, 0, w^2, w, w^2, 1, 0, 1, 0, 0, w, w, w, 1, w^2, w^2, 0, 0, w^2, w ] [ 0, 0, 0, 0, 1, 0, 0, 0, w^2, 0, w^2, w, w^2, 0, 1, w^2, w^2, w^2, w, w^2, 0, w, 1, 0, 1, 1, 1, w, w^2, w, 0, w^2, 1, 0, w^2, 0, w, 0, w, 0, 1, 0, 1, w, 1, w^2, w^2, 1, w^2, 1, w, w^2, 1, 0, 0, w, 0, 0, 1, w, w^2, w, w, 0, w^2, 0, w^2, w^2, w^2, 1, 0, 1, 1, w, 1, 1, 0, 1, w^2, w, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, w^2, 0, w^2, w^2, w, w^2, w, w, 1, w^2, w^2, 1, 0, 1, w, 1, w^2, 1, 1, 1, 0, 0, 0, w, 0, 1, w^2, w, w, 0, 1, 1, w, 0, w, 0, 1, w, 0, w^2, w^2, w^2, 0, w^2, 1, 1, 0, w, 0, w, 1, 0, 0, 1, w, 0, w, w, 1, 0, 1, w^2, 0, 1, 1, 0, w, w, w^2, w^2, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, 0, 1, w, 0, 1, 1, 1, w^2, 0, 0, w^2, 0, 0, w, 0, w, 1, 1, w, 1, 0, 1, w, w^2, w^2, 0, 0, w, 0, 0, w^2, 1, 0, w, 1, w^2, w, w, w, 1, w, w, w, 0, w^2, w^2, w, w^2, 1, w, w, w, w^2, 1, w, w^2, w, w^2, 1, 1, 1, w, w^2, 0, 0, 1, w^2, 0, w, 0, w, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, w, 0, 1, w, 1, 0, 0, 0, w, 1, 0, w^2, 0, 0, w, 1, w^2, 0, 0, w, 0, 1, 0, w^2, w, w, 1, 1, w, 0, 0, w, 0, 1, w^2, 0, w, w, w, w^2, 0, w^2, w^2, w^2, 1, w, w^2, w, w, 0, w^2, w^2, w^2, w, 0, w, w^2, w^2, w, 0, 0, 0, w^2, w, 0, 1, 0, w, 1, w^2, 1, w^2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, w^2, 1, w, w^2, 1, w, w, w^2, w^2, w^2, w^2, 1, 1, w, 1, w^2, w^2, w, 1, w^2, w^2, 1, 1, w, w^2, w^2, w^2, 1, 1, w, 1, w, w^2, w, 1, w, 1, w^2, w, 1, w^2, w, w^2, 1, w, w^2, w^2, w^2, 1, 1, 1, w, w, w^2, w, w, w, w^2, 1, w, w, 1, 1, 1, w^2, 1, w, w, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [80, 9, 49] Linear Code over GF(2^2) Puncturing of [1] at { 81 } last modified: 2009-08-13
Lb(80,9) = 48 is found by taking a subcode of: Lb(80,11) = 48 BZ Ub(80,9) = 54 follows by a one-step Griesmer bound from: Ub(25,8) = 13 is found by considering shortening to: Ub(23,6) = 13 BGV
BZ: E. L. Blokh & V. V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm. 10 (1974) 218-222.
Notes
|