lower bound: | 60 |
upper bound: | 66 |
Construction of a linear code [148,16,60] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [51, 8, 32] Cyclic Linear Code over GF(2^2) CyclicCode of length 51 with generating polynomial x^43 + w^2*x^40 + x^38 + x^37 + x^36 + w*x^35 + x^34 + x^33 + w*x^32 + x^30 + w*x^29 + w*x^28 + w^2*x^26 + w*x^24 + x^22 + w^2*x^21 + x^20 + w*x^19 + w*x^18 + w*x^16 + w^2*x^15 + w*x^13 + w^2*x^12 + w^2*x^11 + w*x^9 + w^2*x^7 + w*x^6 + w*x^5 + w*x^4 + x^3 + w*x + w^2 [3]: [49, 8, 30] Linear Code over GF(2^2) Puncturing of [2] at { 50 .. 51 } [4]: [147, 16, 60] Linear Code over GF(2) ConcatenatedCode of [3] and [1] [5]: [148, 16, 60] Linear Code over GF(2) ExtendCode [4] by 1 last modified: 2002-11-21
Lb(148,16) = 60 is found by truncation of: Lb(150,16) = 62 CZ2 Ub(148,16) = 66 follows by a one-step Griesmer bound from: Ub(81,15) = 33 follows by a one-step Griesmer bound from: Ub(47,14) = 16 follows by a one-step Griesmer bound from: Ub(30,13) = 8 is found by considering shortening to: Ub(28,11) = 8 otherwise adding a parity check bit would contradict: Ub(29,11) = 9 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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