lower bound: | 102 |
upper bound: | 104 |
Construction of a linear code [220,12,102] 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]: [74, 6, 55] Linear Code over GF(2^2) Puncturing of [2] at { 75 .. 78 } [4]: [222, 12, 104] Linear Code over GF(2) ConcatenatedCode of [3] and [1] [5]: [220, 12, 102] Linear Code over GF(2) Puncturing of [4] at { 221 .. 222 } last modified: 2001-01-30
Lb(220,12) = 102 is found by truncation of: Lb(222,12) = 104 BZ Ub(220,12) = 104 follows by a one-step Griesmer bound from: Ub(115,11) = 52 otherwise adding a parity check bit would contradict: Ub(116,11) = 53 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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