lower bound: | 72 |
upper bound: | 72 |
Construction of a linear code [152,9,72] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [51, 5, 36] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 1, w, 0, 0, 0, w^2, 1, w, w^2, w, 0, 0, w, w, 0, w, 1, w, w^2, w^2, 1, 0, w, 0, w, w, 0, 1, w, w^2, w^2, w, 0, w, w, w^2, w^2, 1, 0, w, 1, w, w, w^2, 0, 0, w^2, w ] [ 0, 1, 0, 1, w^2, 0, 0, 1, 1, w^2, 0, 0, 0, w, w, w^2, 0, 1, w^2, 0, w^2, w^2, 1, w^2, 1, 1, w^2, 1, w^2, w, 1, 1, 0, 1, 1, 0, 0, 0, w, 1, w^2, w^2, 0, w^2, 0, 1, 1, 1, w^2, 1, 1 ] [ 0, 0, 1, w, w, 0, 0, w^2, 1, 0, w^2, w, 0, 0, w^2, w, 0, w, 1, w^2, w^2, w^2, 1, 0, w^2, 0, w, w, 0, w^2, w, w^2, w^2, w, w, w, w, w^2, w^2, 0, 0, w, 1, w, w, w^2, 0, 0, w^2, w^2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, w, w^2, w, w^2, w, w, 0, w^2, w^2, 0, 1, w, 1, w, w^2, w, w, 0, 1, w, 1, 1, 0, w, w^2, w, w, 0, w^2, w^2, 0, 1, w, 1, w^2, w^2, 0, 1, w, 0, w^2, 1, w^2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, w, 1, 1, 1, 1, 0, w, w^2, 0, w^2, 1, w^2, w^2, w, 1, 1, 0, w, 1, w^2, w^2, 0, 1, w, 1, 1, 0, w, w, 0, w^2, 1, w^2, w, w, 0, w^2, 1, 0, w, w^2, w, w, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [3]: [153, 10, 72] Linear Code over GF(2) ConcatenatedCode of [2] and [1] [4]: [152, 9, 72] Linear Code over GF(2) Shortening of [3] at { 153 } last modified: 2001-01-30
Lb(152,9) = 72 is found by shortening of: Lb(153,10) = 72 BZ Ub(152,9) = 72 follows by a one-step Griesmer bound from: Ub(79,8) = 36 otherwise adding a parity check bit would contradict: Ub(80,8) = 37 BJV
BZ: E. L. Blokh & V. V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm. 10 (1974) 218-222.
Notes
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