lower bound: | 93 |
upper bound: | 101 |
Construction of a linear code [162,11,93] over GF(3): [1]: [2, 1, 2] Cyclic Linear Code over GF(3) RepetitionCode of length 2 [2]: [160, 10, 93] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^78 + x^77 + 2*x^73 + x^71 + x^70 + x^69 + x^64 + x^62 + x^60 + 2*x^59 + 2*x^58 + 2*x^56 + 2*x^55 + 2*x^54 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^45 + x^42 + 2*x^41 + x^40 + 2*x^39 + x^38 + x^36 + x^32 + x^31 + x^29 + x^28 + x^27 + 2*x^26 + 2*x^25 + x^24 + 2*x^23 + x^22 + 2*x^21 + 2*x^20 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^13 + 2*x^11 + 2*x^10 + 1, 2*x^78 + x^77 + 2*x^75 + x^73 + 2*x^72 + 2*x^71 + x^70 + 2*x^69 + x^68 + 2*x^67 + x^66 + 2*x^65 + 2*x^64 + 2*x^63 + x^62 + x^61 + 2*x^60 + 2*x^58 + 2*x^56 + x^55 + 2*x^54 + x^53 + 2*x^50 + x^49 + x^47 + x^46 + 2*x^45 + 2*x^43 + 2*x^40 + 2*x^37 + x^35 + 2*x^33 + x^31 + 2*x^29 + 2*x^27 + x^24 + 2*x^22 + x^18 + x^17 + 2*x^15 + x^13 + x^9 + 2*x^6 + 2*x^5 + x^4 + x^2 + 2*x + 2 [3]: [160, 11, 91] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^79 + x^77 + 2*x^76 + x^75 + 2*x^74 + x^71 + x^69 + 2*x^68 + x^67 + 2*x^66 + x^65 + x^62 + 2*x^61 + 2*x^60 + 2*x^58 + x^57 + x^56 + x^55 + x^54 + 2*x^53 + x^51 + 2*x^49 + x^48 + 2*x^47 + x^46 + x^45 + 2*x^44 + x^43 + 2*x^41 + 2*x^40 + x^38 + 2*x^37 + 2*x^36 + x^35 + 2*x^34 + x^33 + x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^27 + 2*x^25 + 2*x^24 + x^22 + x^21 + x^20 + x^17 + 2*x^14 + 2*x^11 + 1, 2*x^79 + x^77 + 2*x^76 + x^73 + x^72 + x^71 + 2*x^69 + 2*x^68 + x^66 + x^65 + x^64 + x^63 + x^61 + x^60 + 2*x^59 + 2*x^56 + 2*x^55 + x^53 + 2*x^52 + x^51 + x^50 + x^47 + 2*x^45 + x^44 + x^43 + 2*x^42 + x^41 + x^40 + 2*x^39 + x^38 + x^37 + 2*x^36 + 2*x^35 + x^34 + x^33 + 2*x^32 + 2*x^31 + x^30 + x^29 + 2*x^28 + x^24 + 2*x^23 + x^18 + 2*x^15 + x^14 + x^9 + 2*x^8 + x^7 + x^6 + x^5 + x^2 + x + 1 [4]: [162, 11, 93] Linear Code over GF(3) ConstructionX using [3] [2] and [1] last modified: 2003-09-29
Lb(162,11) = 93 DaH Ub(162,11) = 101 is found by considering shortening to: Ub(160,9) = 101 is found by considering truncation to: Ub(159,9) = 100 Da2
DaH: Rumen Daskalov & Plamen Hristov, New One-Generator Quasi-Cyclic Codes over GF(7), preprint, Oct 2001. R. Daskalov & P Hristov, New One-Generator Quasi-Twisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov, New Quasi-Twisted Degenerate Ternary Linear Codes, preprint, Nov 2001. Email, 2002-2003.
Notes
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