lower bound: | 72 |
upper bound: | 77 |
Construction of a linear code [126,11,72] over GF(3): [1]: [5, 1, 5] Cyclic Linear Code over GF(3) RepetitionCode of length 5 [2]: [121, 10, 72] Cyclic Linear Code over GF(3) CyclicCode of length 121 with generating polynomial x^111 + x^109 + x^108 + x^106 + 2*x^105 + x^104 + x^103 + 2*x^102 + x^100 + x^99 + 2*x^95 + 2*x^94 + x^92 + 2*x^91 + x^90 + x^89 + x^88 + 2*x^86 + x^85 + x^84 + 2*x^83 + x^82 + 2*x^81 + x^79 + 2*x^78 + 2*x^77 + x^76 + x^75 + x^74 + 2*x^72 + 2*x^71 + 2*x^70 + x^69 + 2*x^68 + x^67 + x^66 + 2*x^63 + x^58 + 2*x^57 + x^56 + 2*x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + x^48 + x^47 + 2*x^46 + 2*x^45 + 2*x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + 2*x^36 + x^35 + 2*x^34 + 2*x^33 + x^32 + 2*x^31 + 2*x^30 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + 2*x^19 + 2*x^18 + 2*x^17 + x^13 + 2*x^12 + 2*x^10 + x^8 + 2*x^6 + x^4 + 2*x^3 + 2*x^2 + x + 2 [3]: [121, 11, 67] Cyclic Linear Code over GF(3) CyclicCode of length 121 with generating polynomial x^110 + x^109 + 2*x^108 + x^105 + x^103 + 2*x^102 + x^101 + x^100 + 2*x^99 + 2*x^94 + x^93 + x^92 + 2*x^91 + x^90 + 2*x^89 + x^87 + x^86 + x^84 + 2*x^83 + x^82 + 2*x^81 + x^80 + x^79 + 2*x^78 + x^77 + x^75 + 2*x^74 + 2*x^71 + x^70 + x^68 + x^66 + 2*x^65 + 2*x^64 + 2*x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + 2*x^57 + x^56 + 2*x^55 + 2*x^54 + 2*x^53 + x^52 + x^50 + 2*x^49 + x^48 + 2*x^47 + 2*x^45 + x^44 + x^42 + 2*x^41 + x^39 + 2*x^38 + 2*x^37 + 2*x^36 + x^35 + 2*x^34 + x^33 + x^31 + 2*x^29 + x^27 + x^26 + 2*x^25 + x^22 + 2*x^21 + 2*x^20 + 2*x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^11 + 2*x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1 [4]: [126, 11, 72] Linear Code over GF(3) ConstructionX using [3] [2] and [1] last modified: 2003-09-25
Lb(126,11) = 72 Br2 Ub(126,11) = 77 is found by considering shortening to: Ub(124,9) = 77 LP
LP: Follows from the linear programming bound.
Notes
|