lower bound:  60 
upper bound:  74 
Construction of a linear code [142,26,60] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [140, 25, 59] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 140 with generating polynomials: x^69 + 2*x^68 + x^67 + 2*x^65 + x^64 + 2*x^59 + 2*x^58 + x^56 + x^54 + 2*x^52 + 2*x^51 + x^50 + 2*x^49 + x^48 + 2*x^47 + 2*x^46 + 2*x^45 + x^44 + x^43 + 2*x^42 + 2*x^41 + x^40 + x^39 + x^37 + x^34 + 2*x^30 + x^29 + 2*x^28 + 2*x^27 + x^26 + x^17, x^69 + x^68 + 2*x^66 + x^65 + 2*x^64 + x^63 + x^59 + x^58 + x^57 + x^56 + 2*x^55 + 2*x^53 + 2*x^51 + 2*x^50 + 2*x^48 + x^47 + 2*x^45 + x^44 + x^40 + x^39 + x^37 + x^36 + x^35 + 2*x^33 + x^30 + 2*x^29 + 2*x^28 + 2*x^27 + 2*x^26 + 2*x^24 + 2*x^22 + 2*x^21 + x^20 + 2*x^18 + x^16 + x^15 + x^14 + 2*x^13 + x^11 + x^6 + x^5 + 2*x^4 + x^3 [3]: [140, 25, 59] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 140 with generating polynomials: 2*x^66 + 2*x^63 + x^61 + 2*x^60 + x^59 + 2*x^57 + x^56 + 2*x^55 + 2*x^54 + 2*x^53 + 2*x^52 + x^51 + 2*x^50 + x^49 + x^48 + x^46 + x^43 + 2*x^42 + x^41 + x^37 + 2*x^36 + 2*x^35 + x^33 + x^32 + x^31 + x^30 + 2*x^29 + x^28 + x^27 + 2*x^26 + x^13, x^69 + x^68 + x^67 + x^66 + 2*x^63 + 2*x^62 + 2*x^61 + 2*x^60 + 2*x^59 + 2*x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^49 + 2*x^48 + 2*x^47 + x^43 + 2*x^40 + x^39 + 2*x^37 + 2*x^35 + x^34 + x^33 + x^32 + x^29 + x^27 + 2*x^25 + 2*x^22 + 2*x^20 + 2*x^19 + x^18 + x^15 + 2*x^13 + 2*x^10 + 2*x^9 + 2*x^8 + x^5 + 2*x^2 + x [4]: [140, 26, 58] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 140 with generating polynomials: 2*x^69 + x^67 + x^66 + 2*x^65 + x^64 + 2*x^59 + x^57 + 2*x^56 + 2*x^54 + 2*x^53 + x^51 + x^50 + 2*x^49 + x^48 + 2*x^46 + 2*x^45 + 2*x^43 + x^42 + x^40 + x^38 + x^35 + x^34 + 2*x^33 + 2*x^31 + 2*x^30 + 2*x^28 + x^27 + 2*x^26 + x^5, x^69 + 2*x^68 + 2*x^66 + 2*x^65 + x^63 + x^62 + x^61 + 2*x^60 + 2*x^59 + x^57 + x^56 + x^55 + 2*x^54 + 2*x^53 + 2*x^52 + x^51 + 2*x^50 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + 2*x^41 + 2*x^40 + x^38 + x^36 + 2*x^35 + 2*x^33 + x^32 + 2*x^30 + 2*x^29 + 2*x^28 + x^27 + 2*x^25 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + x^16 + 2*x^13 + x^10 + x^9 + x^5 + 2*x^2 [5]: [142, 26, 60] Linear Code over GF(3) ConstructionXX using [4] [3] [2] [1] and [1] last modified: 20210826
Lb(142,26) = 55 Vx Ub(142,26) = 74 is found by considering shortening to: Ub(139,23) = 74 Da2
Vx: From the VarshamovGilbert bound together with construction X,
Notes
