lower bound: | 76 |
upper bound: | 83 |
Construction of a linear code [135,11,76] over GF(3): [1]: [5, 1, 5] Cyclic Linear Code over GF(3) RepetitionCode of length 5 [2]: [12, 6, 6] Linear Code over GF(3) Extend the QRCode over GF(3)of length 11 [3]: [11, 5, 6] Cyclic Linear Code over GF(3) Shortening of [2] at { 12 } [4]: [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 [5]: [121, 6, 76] Cyclic Linear Code over GF(3) CyclicCode of length 121 with generating polynomial x^115 + 2*x^114 + x^113 + 2*x^112 + 2*x^111 + 2*x^110 + 2*x^109 + 2*x^107 + 2*x^106 + 2*x^105 + x^101 + x^100 + x^97 + 2*x^96 + 2*x^95 + x^93 + 2*x^91 + 2*x^89 + x^87 + x^84 + x^83 + x^82 + x^81 + 2*x^78 + x^76 + x^75 + x^74 + 2*x^72 + x^71 + x^70 + x^68 + x^67 + x^65 + 2*x^64 + x^63 + x^60 + 2*x^57 + 2*x^56 + 2*x^54 + 2*x^51 + x^50 + x^48 + x^47 + x^46 + 2*x^45 + x^44 + 2*x^43 + x^40 + x^39 + 2*x^38 + 2*x^37 + 2*x^36 + x^35 + 2*x^34 + x^32 + 2*x^31 + 2*x^28 + 2*x^27 + x^26 + 2*x^24 + x^23 + 2*x^22 + x^21 + 2*x^19 + x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^12 + x^11 + 2*x^9 + x^6 + x^4 + x^2 + x + 2 [6]: [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 [7]: [137, 11, 78] Linear Code over GF(3) ConstructionXX using [6] [5] [4] [3] and [1] [8]: [135, 11, 76] Linear Code over GF(3) Puncturing of [7] at { 136 .. 137 } last modified: 2003-10-30
Lb(135,11) = 75 is found by truncation of: Lb(138,11) = 78 Bou Ub(135,11) = 83 is found by considering shortening to: Ub(133,9) = 83 Da2
Da2: R.N. Daskalov, The linear programming bound for ternary linear codes, p. 423 in: IEEE International Symposium on Information Theory, Trondheim, 1994.
Notes
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