lower bound: | 100 |
upper bound: | 106 |
Construction of a linear code [168,10,100] 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, 6, 102] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^79 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + 2*x^73 + 2*x^71 + x^70 + x^69 + 2*x^68 + x^67 + 2*x^66 + 2*x^65 + x^63 + x^62 + x^61 + x^60 + 2*x^58 + x^57 + x^56 + x^53 + x^52 + x^51 + x^50 + x^49 + 2*x^48 + 2*x^46 + 2*x^45 + 2*x^44 + x^42 + 2*x^40 + 2*x^39 + x^38 + x^37 + x^36 + x^35 + 2*x^34 + x^33 + 2*x^32 + x^31 + 2*x^29 + 2*x^27 + 2*x^26 + x^25 + 2*x^24 + 2*x^23 + 2*x^21 + x^20 + 2*x^18 + 2*x^17 + x^16 + x^14 + 2*x^13 + x^12 + 2*x^11 + 2*x^9 + 2*x^6 + x^5, x^79 + 2*x^78 + 2*x^76 + x^75 + x^74 + x^73 + x^72 + x^70 + x^69 + 2*x^68 + 2*x^67 + x^66 + 2*x^65 + 2*x^64 + x^63 + 2*x^62 + x^60 + x^59 + x^58 + 2*x^53 + x^52 + x^51 + x^50 + 2*x^49 + 2*x^46 + x^45 + x^44 + 2*x^42 + x^41 + 2*x^40 + 2*x^38 + 2*x^37 + x^33 + x^32 + x^31 + x^29 + 2*x^27 + 2*x^22 + 2*x^21 + x^20 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^12 + 2*x^8 + x^7 + 2*x^6 + x^5 + x^4 + x^3 + 2*x^2 + x [4]: [160, 10, 96] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^79 + x^78 + 2*x^77 + 2*x^76 + x^75 + 2*x^73 + 2*x^71 + 2*x^68 + x^67 + x^66 + 2*x^65 + 2*x^64 + x^62 + x^60 + x^59 + x^58 + x^57 + x^55 + 2*x^53 + x^51 + 2*x^50 + 2*x^47 + 2*x^46 + 2*x^45 + 2*x^44 + x^43 + x^42 + x^41 + x^36 + 2*x^35 + 2*x^33 + 2*x^27 + x^26 + x^24 + x^23 + 2*x^22 + x^20 + 2*x^18 + x^17 + 2*x^16 + x^15 + x^14 + x^13 + 2*x^12 + 2*x^11 + 2*x^10 + x^9, x^79 + 2*x^78 + x^77 + 2*x^75 + x^74 + 2*x^73 + 2*x^72 + x^71 + 2*x^70 + x^68 + 2*x^67 + x^64 + x^62 + x^61 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + 2*x^51 + 2*x^49 + 2*x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + 2*x^39 + x^35 + x^34 + x^33 + x^32 + x^30 + x^29 + 2*x^28 + 2*x^25 + x^23 + 2*x^21 + 2*x^16 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 1 [5]: [170, 10, 102] Linear Code over GF(3) ConstructionX using [4] [3] and [2] [6]: [168, 10, 100] Linear Code over GF(3) Puncturing of [5] at { 169 .. 170 } last modified: 2007-07-30
Lb(168,10) = 99 MST Ub(168,10) = 106 is found by considering shortening to: Ub(166,8) = 106 Da2
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
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