lower bound:  36 
upper bound:  38 
Construction of a linear code [86,12,36] over GF(2): [1]: [2, 1, 2] Cyclic Linear Code over GF(2) RepetitionCode of length 2 [2]: [84, 11, 36] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 84 with generating polynomials: x^18 + x^17 + x^15 + x^13 + x^11 + 1, x^18 + x^12 + x^8 + x^7 + x^5 + x^2, x^20 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^9 + x^5 + x^2, x^20 + x^19 + x^18 + x^17 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 [3]: [84, 12, 34] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 84 stacked to height 2 with generating polynomials: x^18 + x^17 + x^15 + x^13 + x^11 + 1, x^18 + x^12 + x^8 + x^7 + x^5 + x^2, x^20 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^9 + x^5 + x^2, x^20 + x^19 + x^18 + x^17 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2, 0, 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^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 [4]: [86, 12, 36] Linear Code over GF(2) ConstructionX using [3] [2] and [1] last modified: 20030402
Lb(86,12) = 36 GW2 Ub(86,12) = 38 follows by a onestep Griesmer bound from: Ub(47,11) = 18 otherwise adding a parity check bit would contradict: Ub(48,11) = 19 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
