lower bound: | 33 |
upper bound: | 38 |
Construction of a linear code [92,17,33] over GF(2): [1]: [93, 17, 34] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 93 stacked to height 3 with generating polynomials: x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^28 + x^26 + x^23 + x^21 + x^20 + x^19 + x^18 + x^17 + x^15 + x^7, x^29 + x^28 + x^27 + x^22 + x^21 + x^20 + x^19 + x^16 + x^15 + x^14 + x^13 + x^11 + x^6 + x^4 + x^2 + 1, x^30 + x^29 + x^26 + x^24 + x^23 + x^18 + x^16 + x^15 + x^13 + x^12 + x^11 + x^8 + x^6 + 1 [2]: [92, 17, 33] Linear Code over GF(2) Puncturing of [1] at { 93 } last modified: 2006-09-15
Lb(92,17) = 33 is found by truncation of: Lb(93,17) = 34 Ch3 Ub(92,17) = 38 follows by a one-step Griesmer bound from: Ub(53,16) = 18 is found by considering shortening to: Ub(51,14) = 18 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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