lower bound:  73 
upper bound:  91 
Construction of a linear code [170,27,73] over GF(3): [1]: [12, 6, 6] Linear Code over GF(3) Extend the QRCode over GF(3)of length 11 [2]: [10, 4, 6] Linear Code over GF(3) Shortening of [1] at { 11 .. 12 } [3]: [160, 23, 73] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^78 + x^76 + x^75 + x^74 + x^73 + x^72 + 2*x^70 + x^69 + 2*x^68 + 2*x^67 + 2*x^65 + 2*x^64 + 2*x^63 + x^61 + 2*x^60 + 2*x^59 + x^58 + 2*x^57 + x^56 + x^55 + x^54 + 2*x^53 + 2*x^52 + 2*x^51 + x^49 + 2*x^48 + 2*x^47 + 2*x^46 + x^45 + x^44 + 2*x^42 + 2*x^41 + 2*x^40 + x^39 + 2*x^38 + x^37 + x^36 + x^35 + 2*x^32 + x^30 + x^28 + x^27 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^13, 2*x^79 + 2*x^78 + x^76 + 2*x^75 + 2*x^74 + x^72 + x^71 + x^70 + 2*x^68 + 2*x^67 + x^66 + 2*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + x^53 + x^50 + 2*x^49 + x^47 + x^46 + x^45 + x^44 + 2*x^43 + x^42 + x^40 + x^39 + x^38 + x^36 + 2*x^33 + 2*x^32 + 2*x^31 + 2*x^30 + x^29 + x^28 + 2*x^27 + 2*x^25 + x^24 + x^23 + x^22 + 2*x^19 + 2*x^18 + 2*x^16 + 2*x^15 + x^12 + 2*x^11 + x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^4 + x^3 + 2*x [4]: [160, 27, 67] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^77 + 2*x^76 + x^75 + 2*x^74 + 2*x^73 + x^72 + 2*x^71 + x^69 + x^68 + 2*x^66 + 2*x^65 + x^64 + 2*x^62 + 2*x^61 + 2*x^59 + 2*x^58 + x^55 + 2*x^54 + x^53 + x^52 + 2*x^51 + x^50 + x^49 + x^45 + x^43 + 2*x^41 + 2*x^40 + x^39 + x^38 + 2*x^36 + 2*x^31 + x^30 + x^29 + 2*x^28 + 2*x^27 + x^12, 2*x^78 + 2*x^76 + x^74 + x^73 + x^71 + 2*x^69 + 2*x^68 + x^67 + 2*x^65 + x^64 + x^63 + 2*x^62 + x^59 + 2*x^58 + 2*x^57 + x^56 + 2*x^55 + x^54 + x^53 + 2*x^52 + 2*x^51 + x^50 + x^49 + 2*x^48 + x^47 + x^46 + 2*x^44 + x^43 + x^40 + x^39 + 2*x^37 + x^36 + 2*x^35 + x^34 + 2*x^33 + 2*x^31 + 2*x^29 + 2*x^26 + 2*x^25 + 2*x^24 + x^23 + 2*x^20 + 2*x^19 + 2*x^17 + 2*x^14 + x^12 + x^10 + x^7 + 2*x^6 + 2*x^2 + 1 [5]: [170, 27, 73] Linear Code over GF(3) ConstructionX using [4] [3] and [2] last modified: 20210826
Lb(170,27) = 72 is found by taking a subcode of: Lb(170,28) = 72 GW2 Ub(170,27) = 91 is found by considering shortening to: Ub(167,24) = 91 Da9
GW2: M. Grassl & G. White, New Codes from Chains of Quasicyclic Codes, ISIT 2005.
Notes
