lower bound: | 34 |
upper bound: | 39 |
Construction of a linear code [96,18,34] over GF(2): [1]: [3, 1, 3] Cyclic Linear Code over GF(2) RepetitionCode of length 3 [2]: [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 [3]: [93, 18, 31] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 93 stacked to height 4 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, 0, 0, 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, 0, 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 [4]: [96, 18, 34] Linear Code over GF(2) ConstructionX using [3] [2] and [1] last modified: 2009-12-18
Lb(96,18) = 33 is found by shortening of: Lb(98,20) = 33 is found by truncation of: Lb(99,20) = 34 CZ Ub(96,18) = 39 is found by considering shortening to: Ub(93,15) = 39 Bro
CZ: Chen Zhi, Six new binary quasi-cyclic codes, IEEE Trans. Inf. Theory 40 (1994) 1666-1667.
Notes
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