lower bound: | 108 |
upper bound: | 112 |
Construction of a linear code [177,9,108] over GF(3): [1]: [2, 1, 2] Cyclic Linear Code over GF(3) RepetitionCode of length 2 [2]: [16, 5, 9] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1, 2 ] [ 0, 1, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 2, 1, 2 ] [ 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 0, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1 ] [3]: [15, 4, 9] Linear Code over GF(3) Shortening of [2] at { 16 } [4]: [160, 8, 99] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: x^79 + x^78 + x^76 + x^74 + 2*x^73 + x^71 + 2*x^69 + 2*x^68 + 2*x^65 + 2*x^64 + x^63 + x^62 + 2*x^61 + 2*x^59 + 2*x^58 + x^57 + x^56 + x^53 + x^51 + x^48 + x^47 + 2*x^46 + x^44 + 2*x^41 + x^40 + x^38 + x^37 + 2*x^35 + x^34 + x^32 + 2*x^31 + x^30 + x^29 + 2*x^28 + 2*x^27 + x^26 + x^25 + 2*x^23 + 2*x^22 + 2*x^21 + x^20 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + 2*x^10 + x^8 + 1, x^79 + 2*x^77 + 2*x^76 + x^75 + x^74 + 2*x^72 + 2*x^71 + x^70 + 2*x^68 + 2*x^67 + x^65 + 2*x^63 + x^61 + 2*x^60 + x^58 + x^57 + x^55 + x^54 + 2*x^53 + 2*x^52 + x^51 + 2*x^49 + 2*x^48 + 2*x^46 + x^45 + 2*x^42 + 2*x^41 + x^40 + x^38 + x^37 + x^36 + x^34 + 2*x^33 + x^32 + 2*x^31 + x^30 + x^28 + x^27 + x^26 + 2*x^25 + 2*x^24 + x^21 + 2*x^19 + x^18 + 2*x^17 + x^15 + 2*x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^5 + x^4 + x^3 + x^2 + 2*x [5]: [160, 5, 106] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^79 + x^78 + x^76 + 2*x^72 + 2*x^69 + 2*x^68 + 2*x^67 + x^64 + x^63 + x^61 + 2*x^60 + 2*x^59 + x^58 + 2*x^56 + x^55 + 2*x^54 + 2*x^53 + 2*x^51 + 2*x^49 + x^48 + 2*x^45 + x^44 + x^43 + x^42 + x^41 + 2*x^39 + x^37 + x^35 + x^34 + x^33 + 2*x^32 + x^31 + x^30 + 2*x^29 + 2*x^28 + 2*x^27 + x^26 + x^25 + x^22 + 2*x^20 + 2*x^19 + x^17 + 2*x^16 + 2*x^14 + 2*x^13 + x^12 + 2*x^11 + x^10 + 2*x^9 + x^7 + x^6 + 2*x^5 + 1, x^79 + x^78 + x^75 + 2*x^73 + 2*x^72 + x^70 + 2*x^69 + 2*x^67 + 2*x^66 + x^65 + 2*x^64 + x^63 + 2*x^62 + x^60 + x^59 + 2*x^58 + x^53 + 2*x^52 + x^51 + x^49 + 2*x^45 + 2*x^42 + 2*x^41 + 2*x^40 + x^37 + x^36 + x^34 + 2*x^33 + 2*x^32 + x^31 + 2*x^29 + x^28 + 2*x^27 + 2*x^26 + 2*x^24 + 2*x^22 + x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + x^10 + x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + 2*x + 2 [6]: [160, 9, 97] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 160 with generating polynomials: 2*x^79 + x^76 + x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + x^69 + 2*x^65 + x^64 + 2*x^63 + 2*x^61 + 2*x^60 + x^59 + x^57 + 2*x^56 + 2*x^55 + 2*x^54 + x^51 + x^50 + x^49 + 2*x^48 + 2*x^46 + 2*x^45 + 2*x^41 + x^38 + 2*x^37 + 2*x^36 + x^35 + 2*x^34 + 2*x^33 + 2*x^31 + x^29 + 2*x^27 + x^25 + x^24 + 2*x^22 + x^21 + 2*x^20 + 2*x^19 + x^18 + 2*x^17 + x^15 + 2*x^14 + 2*x^13 + x^12 + 2*x^10 + 2*x^9 + 1, 2*x^77 + x^76 + 2*x^75 + 2*x^72 + x^71 + 2*x^70 + 2*x^69 + x^68 + x^65 + x^64 + x^61 + x^58 + 2*x^57 + 2*x^56 + x^54 + 2*x^52 + 2*x^49 + x^48 + x^47 + x^45 + x^44 + x^43 + 2*x^41 + x^38 + 2*x^37 + x^34 + x^32 + x^30 + x^29 + 2*x^28 + x^26 + 2*x^24 + 2*x^23 + 2*x^22 + 2*x^19 + 2*x^17 + 2*x^16 + 2*x^13 + x^11 + 2*x^10 + x^8 + x^7 + x^6 + x^4 + 2*x^3 + 2*x + 2 [7]: [177, 9, 108] Linear Code over GF(3) ConstructionXX using [6] [5] [4] [3] and [1] last modified: 2003-10-10
Lb(177,9) = 107 is found by truncation of: Lb(178,9) = 108 MST Ub(177,9) = 112 is found by considering truncation to: Ub(176,9) = 111 Gur
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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