lower bound: | 110 |
upper bound: | 110 |
Construction of a linear code [232,12,110] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [78, 6, 56] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^2, w^2, w^2, w, 0, 1, 0, w^2, 1, 1, 1, w^2, w^2, w^2, 1, 1, w^2, w^2, 1, w, w, w^2, 0, w, 0, 0, 1, 1, w^2, 0, w^2, w, w^2, w^2, 1, 1, 0, 0, w^2, 1, w^2, 1, 0, w^2, 1, 0, w, 0, w, w, w^2, w, w, w^2, 0, w^2, 0, 0, w^2, w, 1, w, w, 1, w^2, w, w^2, 0, 0, w^2, 0, w ] [ 0, 1, 0, 0, 0, 0, 1, w, w, 0, w, w, 1, 1, 1, w^2, w^2, 0, w, w, 1, w^2, 0, w, 1, w, 1, w^2, w^2, w^2, w, 0, w, w^2, 0, w^2, 1, 0, w^2, 0, 1, w^2, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, w^2, w, w^2, 1, w^2, 0, 1, w^2, w^2, 1, w^2, 0, 1, 0, 0, w, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, w^2 ] [ 0, 0, 1, 0, 0, 0, 1, 0, w^2, 1, 0, 0, w, 0, w^2, w^2, 1, w, 1, w^2, 0, w^2, w, 1, 0, w, 1, 0, w^2, 0, w^2, w, w, 0, w, 0, w, w, 1, w^2, w, w^2, w^2, 1, 1, w^2, 0, w, 1, 0, w^2, 1, w, w^2, 1, 0, 0, 0, w^2, 0, w^2, w, 1, w^2, 1, w, w, w^2, 1, w^2, 1, w^2, 1, w^2, w^2, 1, 1, 0 ] [ 0, 0, 0, 1, 0, 0, w, w^2, w, w, 1, w^2, 0, 0, w^2, 0, 0, w^2, 0, w^2, 0, w^2, 1, 0, w, 1, w^2, w^2, 0, w, 0, w^2, 1, 1, w, w, w, w^2, 0, w, 0, 1, w^2, w^2, w^2, w, 1, w^2, w, w^2, w^2, w^2, 0, w, w, 0, w, 1, 1, 1, 0, 1, w, 1, 1, 0, 1, w^2, w, w, 1, 0, 1, 1, w^2, 1, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, w, w^2, w, w, 1, w^2, 0, 0, w^2, 0, 0, w^2, 0, w^2, 0, w^2, 1, 0, w, 1, w^2, w^2, 0, w, 0, w^2, 1, 1, w, w, w, w^2, 0, w, 0, 1, w^2, w^2, w^2, w, 1, w^2, w, w^2, w^2, w^2, 0, w, w, 0, w, 1, 1, 1, 0, 1, w, 1, 1, 0, 1, w^2, w, w, 1, 0, 1, 1, w^2, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 1, 1, w^2, 0, w, 0, 1, w, w, w, 1, 1, 1, w, w, 1, 1, w, w^2, w^2, 1, 0, w^2, 0, 0, w, w, 1, 0, 1, w^2, 1, w^2, w, w, 0, 0, 1, w, 1, w, 0, 1, w, 0, w^2, 0, w^2, w^2, 1, w^2, w^2, 1, 0, 1, 0, 0, 1, w^2, w, w^2, w^2, w, 1, w^2, 1, 0, 0, 1, 0, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; [3]: [234, 12, 112] Linear Code over GF(2) ConcatenatedCode of [2] and [1] [4]: [232, 12, 110] Linear Code over GF(2) Puncturing of [3] at { 233 .. 234 } last modified: 2001-01-30
Lb(232,12) = 110 is found by truncation of: Lb(234,12) = 112 BZ Ub(232,12) = 110 otherwise adding a parity check bit would contradict: Ub(233,12) = 111 BK
BZ: E. L. Blokh & V. V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm. 10 (1974) 218-222.
Notes
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