lower bound: | 96 |
upper bound: | 105 |
Construction of a linear code [168,11,96] over GF(3): [1]: [12, 6, 6] Linear Code over GF(3) Extend the QRCode over GF(3)of length 11 [2]: [11, 6, 5] Cyclic Linear Code over GF(3) Puncturing of [1] at { 12 } [3]: [8, 3, 5] Linear Code over GF(3) Shortening of [2] at { 9 .. 11 } [4]: [160, 8, 96] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^79 + x^78 + 2*x^77 + 2*x^75 + 2*x^73 + x^72 + 2*x^71 + 2*x^69 + x^68 + 2*x^67 + x^64 + 2*x^63 + 2*x^61 + x^59 + 2*x^58 + 2*x^57 + x^54 + 2*x^53 + 2*x^51 + x^50 + x^47 + 2*x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + 2*x^39 + x^38 + 2*x^35 + 2*x^34 + x^32 + x^30 + 2*x^27 + 2*x^25 + 2*x^23 + x^22 + 2*x^21 + 2*x^20 + x^15 + x^14 + 2*x^12 + 2*x^9 + x^8 + 1, 2*x^79 + 2*x^77 + x^75 + x^74 + 2*x^73 + x^72 + 2*x^71 + 2*x^69 + x^68 + 2*x^67 + x^66 + 2*x^65 + 2*x^64 + x^63 + x^61 + x^57 + 2*x^55 + 2*x^54 + x^53 + 2*x^51 + 2*x^50 + 2*x^49 + x^42 + x^41 + 2*x^40 + x^39 + x^38 + 2*x^37 + x^36 + 2*x^35 + 2*x^34 + x^33 + x^32 + 2*x^31 + 2*x^30 + x^29 + x^28 + x^26 + x^25 + x^24 + 2*x^23 + x^22 + x^21 + x^20 + x^18 + x^16 + x^15 + x^14 + 2*x^13 + 2*x^12 + 2*x^11 + x^9 + 2*x^8 + 2*x^7 + 2*x^6 + x + 2 [5]: [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 [6]: [168, 11, 96] Linear Code over GF(3) ConstructionX using [5] [4] and [3] last modified: 2003-09-29
Lb(168,11) = 96 GW2 Ub(168,11) = 105 follows by a one-step Griesmer bound from: Ub(62,10) = 35 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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