lower bound:  90 
upper bound:  103 
Construction of a linear code [177,18,90] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [176, 17, 90] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 176 with generating polynomials: 2*x^87 + x^86 + x^82 + x^81 + x^79 + x^77 + x^76 + x^75 + x^74 + 2*x^73 + 2*x^72 + x^69 + 2*x^68 + 2*x^66 + x^62 + x^61 + x^60 + 2*x^59 + 2*x^58 + x^57 + x^56 + 2*x^55 + x^54 + 2*x^53 + x^52 + x^51 + x^49 + 2*x^47 + x^46 + x^45 + 2*x^44 + 2*x^43 + x^42 + x^41 + x^40 + 2*x^37 + 2*x^36 + x^34 + x^33 + x^31 + 2*x^29 + x^28 + x^27 + x^25 + 2*x^24 + x^23 + x^21 + 2*x^20 + x^19 + 2*x^17 + x^15, 2*x^87 + 2*x^85 + x^84 + x^83 + 2*x^81 + 2*x^80 + 2*x^79 + 2*x^78 + 2*x^76 + x^75 + x^73 + x^72 + x^71 + 2*x^69 + x^65 + x^64 + x^62 + 2*x^61 + 2*x^60 + x^57 + 2*x^54 + x^53 + 2*x^51 + x^50 + 2*x^48 + x^47 + x^46 + 2*x^44 + x^43 + x^42 + x^41 + 2*x^40 + 2*x^39 + 2*x^37 + x^33 + x^32 + 2*x^29 + 2*x^28 + 2*x^27 + x^26 + 2*x^24 + 2*x^23 + x^22 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + x^11 + x^10 + x^7 + 2*x^6 + 2*x^4 + x^3 + x^2 + 2*x + 2 [3]: [176, 18, 89] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 176 with generating polynomials: x^85 + 2*x^84 + x^83 + 2*x^82 + x^81 + x^80 + x^78 + 2*x^77 + x^76 + x^75 + 2*x^72 + x^71 + x^69 + x^66 + 2*x^64 + 2*x^62 + x^60 + 2*x^59 + x^56 + 2*x^55 + 2*x^52 + x^51 + x^50 + x^48 + 2*x^47 + x^46 + 2*x^43 + x^42 + 2*x^39 + 2*x^38 + 2*x^37 + 2*x^36 + 2*x^32 + 2*x^31 + 2*x^30 + x^29 + 2*x^28 + 2*x^27 + x^26 + x^25 + x^24 + 2*x^22 + 2*x^21 + 2*x^20 + x^19 + x^15, x^87 + 2*x^85 + 2*x^82 + 2*x^81 + 2*x^80 + x^77 + x^76 + x^75 + 2*x^74 + 2*x^72 + 2*x^71 + x^70 + x^69 + x^68 + 2*x^67 + x^66 + 2*x^65 + x^64 + x^63 + x^61 + 2*x^60 + 2*x^59 + 2*x^57 + x^55 + x^53 + x^52 + x^50 + x^49 + x^47 + x^46 + x^42 + 2*x^41 + x^39 + x^38 + 2*x^37 + x^36 + x^34 + x^32 + 2*x^31 + 2*x^29 + x^26 + x^25 + x^23 + x^22 + 2*x^21 + x^16 + 2*x^15 + x^13 + x^12 + 2*x^10 + 2*x^9 + x^8 + 2*x^7 + x^6 + x^5 + 2*x^4 + x^3 + 2 [4]: [177, 18, 90] Linear Code over GF(3) ConstructionX using [3] [2] and [1] last modified: 20210825
Lb(177,18) = 88 is found by shortening of: Lb(179,20) = 88 is found by truncation of: Lb(184,20) = 93 XX Ub(177,18) = 103 is found by considering shortening to: Ub(176,17) = 103 is found by considering truncation to: Ub(175,17) = 102 Da2
XX:
Notes
