lower bound: | 54 |
upper bound: | 58 |
Construction of a linear code [132,16,54] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [44, 8, 27] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 1, w, w, w^2, 1, 1, 1, 0, w^2, w, w^2, w^2, w, 0, w, w^2, 0, w^2, w, w, w^2, w, 0, 1, 1, 1, w, w^2, w^2, 1, w^2, w, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 1, w^2, 1, w^2, w^2, 1, 1, 0, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w, w^2, w^2, w, w^2, w, 1, 0, 0, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 1, w^2, 1, w^2, w^2, 1, 1, 0, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w, w^2, w^2, w, w^2, w, 1, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 1, w^2, 1, w^2, w^2, 1, 1, 0, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w, w^2, w^2, w, w^2, w, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, w, w^2, w, w, w^2, w^2, 0, w, 1, 0, 1, w, w, w, w^2, 0, w^2, w, 0, 1, 1, w, w, 1, w, 1, w^2, 0, 0, 0, w^2, 0, 0, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, w, w^2, w, w, w^2, w^2, 0, w, 1, 0, 1, w, w, w, w^2, 0, w^2, w, 0, 1, 1, w, w, 1, w, 1, w^2, 0, 0, 0, w^2, 0, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, w, w^2, w, w, w^2, w^2, 0, w, 1, 0, 1, w, w, w, w^2, 0, w^2, w, 0, 1, 1, w, w, 1, w, 1, w^2, 0, 0, 0, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 1, w, w, w^2, 1, 1, 1, 0, w^2, w, w^2, w^2, w, 0, w, w^2, 0, w^2, w, w, w^2, w, 0, 1, 1, 1, w, w^2, w^2, 1, w^2, w, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [3]: [132, 16, 54] Linear Code over GF(2) ConcatenatedCode of [2] and [1] last modified: 2002-11-21
Lb(132,16) = 53 XB Ub(132,16) = 58 follows by a one-step Griesmer bound from: Ub(73,15) = 29 follows by a one-step Griesmer bound from: Ub(43,14) = 14 is found by considering shortening to: Ub(42,13) = 14 otherwise adding a parity check bit would contradict: Ub(43,13) = 15 Ja
XB:
Notes
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