lower bound: | 14 |
upper bound: | 16 |
Construction of a linear code [48,17,14] over GF(2): [1]: [16, 1, 16] Cyclic Linear Code over GF(2) RepetitionCode of length 16 [2]: [16, 8, 7] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 0, 1, 0, w^2, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, 1, w^2, 1, w^2, w^2, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, w^2, 1, 1, 0, w, w^2, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, w^2, w^2, w, 1, w, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, w, w^2, w^2, w, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, w^2, w^2, w, w, w^2, 1, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, w^2, w, w^2, 0, 0, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, w^2, 1, w, w, w^2, 1, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; [3]: [3, 3, 1] Cyclic Linear Code over GF(2) UniverseCode of length 3 [4]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [5]: [48, 17, 14] Linear Code over GF(2) ZinovievCode using inner codes: [4] [3], outer codes: [2] [1] last modified: 2001-01-30
Lb(48,17) = 14 BZ Ub(48,17) = 16 follows by a one-step Griesmer bound from: Ub(31,16) = 8 follows by a one-step Griesmer bound from: Ub(22,15) = 4 follows by a one-step Griesmer bound from: Ub(17,14) = 2 is found by considering shortening to: Ub(8,5) = 2 is found by construction B: [consider deleting the (at most) 4 coordinates of a word in the dual]
Notes
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