lower bound:  70 
upper bound:  87 
Construction of a linear code [164,27,70] over GF(3): [1]: [4, 3, 2] Cyclic Linear Code over GF(3) Dual of the RepetitionCode of length 4 [2]: [160, 24, 72] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^79 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + x^73 + x^71 + 2*x^70 + x^69 + x^68 + 2*x^67 + 2*x^66 + x^63 + x^62 + 2*x^60 + x^59 + x^57 + 2*x^56 + x^54 + x^53 + x^52 + x^51 + 2*x^49 + 2*x^48 + x^46 + x^45 + 2*x^42 + 2*x^39 + 2*x^38 + 2*x^37 + 2*x^36 + x^35 + x^34 + 2*x^32 + x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^27 + x^26 + 2*x^25 + x^14, x^77 + 2*x^74 + 2*x^73 + 2*x^72 + x^71 + 2*x^70 + x^69 + x^67 + 2*x^66 + x^65 + x^64 + x^62 + x^61 + 2*x^58 + 2*x^57 + 2*x^55 + x^54 + 2*x^53 + 2*x^52 + 2*x^51 + 2*x^49 + 2*x^48 + 2*x^44 + x^40 + 2*x^39 + x^37 + x^35 + 2*x^34 + x^33 + x^32 + 2*x^30 + x^29 + x^28 + x^27 + 2*x^26 + x^25 + x^24 + x^21 + 2*x^20 + 2*x^19 + x^18 + x^17 + 2*x^15 + x^14 + 2*x^13 + x^10 + x^9 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x + 1 [3]: [160, 27, 68] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^79 + 2*x^78 + x^77 + x^76 + x^75 + 2*x^74 + x^73 + x^72 + 2*x^70 + x^68 + 2*x^67 + x^66 + x^65 + 2*x^63 + 2*x^62 + 2*x^58 + 2*x^57 + 2*x^55 + 2*x^54 + 2*x^53 + x^52 + x^51 + x^50 + 2*x^49 + x^47 + 2*x^46 + x^44 + x^43 + x^42 + x^41 + 2*x^40 + x^39 + x^38 + x^37 + 2*x^35 + x^34 + x^32 + x^31 + x^29 + 2*x^27 + 2*x^26 + 1, 2*x^79 + 2*x^77 + 2*x^75 + 2*x^74 + 2*x^70 + x^68 + x^66 + x^62 + 2*x^60 + x^58 + x^57 + 2*x^54 + 2*x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + 2*x^47 + 2*x^46 + 2*x^45 + x^44 + x^43 + x^42 + x^41 + 2*x^40 + x^38 + 2*x^37 + x^36 + x^35 + 2*x^34 + x^32 + x^31 + 2*x^29 + x^28 + x^27 + x^26 + 2*x^25 + x^24 + x^23 + 2*x^22 + x^21 + x^20 + x^17 + x^15 + x^14 + 2*x^13 + x^12 + x^11 + x^9 + 2*x^8 + x^7 + 2*x^5 + 2*x^4 + x^3 + 2*x [4]: [164, 27, 70] Linear Code over GF(3) ConstructionX using [3] [2] and [1] last modified: 20210826
Lb(164,27) = 69 is found by shortening of: Lb(165,28) = 69 GW2 Ub(164,27) = 87 is found by considering shortening to: Ub(161,24) = 87 Da9
GW2: M. Grassl & G. White, New Codes from Chains of Quasicyclic Codes, ISIT 2005.
Notes
