lower bound: | 36 |
upper bound: | 40 |
Construction of a linear code [96,17,36] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [93, 15, 36] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 93 with generating polynomials: 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, 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 [4]: [96, 17, 36] Linear Code over GF(2) ConstructionX using [3] [2] and [1] last modified: 2006-09-15
Lb(96,17) = 36 Ch3 Ub(96,17) = 40 follows by a one-step Griesmer bound from: Ub(55,16) = 20 follows by a one-step Griesmer bound from: Ub(34,15) = 10 follows by a one-step Griesmer bound from: Ub(23,14) = 5 follows by a one-step Griesmer bound from: Ub(17,13) = 2 is found by considering shortening to: Ub(16,12) = 2 is found by construction B: [consider deleting the (at most) 8 coordinates of a word in the dual]
Notes
|