lower bound: | 63 |
upper bound: | 68 |
Construction of a linear code [152,16,63] over GF(2): [1]: [153, 16, 64] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 153 with generating polynomials: x^43 + x^39 + x^36 + x^32 + x^28 + x^26 + x^20 + x^19 + x^18 + x^17 + x^15 + x^11 + x^5 + x^3 + x + 1, x^45 + x^43 + x^41 + x^40 + x^38 + x^37 + x^36 + x^35 + x^34 + x^30 + x^29 + x^28 + x^27 + x^26 + x^23 + x^19 + x^18 + x^13 + x^12 + x^10 + x^7 + x^4 + x^3 + 1, x^46 + x^45 + x^44 + x^43 + x^42 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^32 + x^31 + x^30 + x^29 + x^27 + x^25 + x^24 + x^21 + x^20 + x^19 + x^17 + x^15 + x^14 + x^13 + x^11 + x^9 + x^7 + x^6 + x^5 + x + 1 [2]: [152, 16, 63] Linear Code over GF(2) Puncturing of [1] at { 153 } last modified: 2001-01-30
Lb(152,16) = 63 is found by truncation of: Lb(153,16) = 64 CZ Ub(152,16) = 68 follows by a one-step Griesmer bound from: Ub(83,15) = 34 follows by a one-step Griesmer bound from: Ub(48,14) = 17 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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