lower bound: | 135 |
upper bound: | 138 |
Construction of a linear code [213,8,135] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [212, 204, 2] Linear Code over GF(3) Dual of [8] [3]: [212, 7, 135] Linear Code over GF(3) The intersection of [8] and [2] [4]: [2, 1, 2] Cyclic Linear Code over GF(3) RepetitionCode of length 2 [5]: [208, 7, 132] Quasicyclic of degree 8 Linear Code over GF(3) QuasiCyclicCode of length 208 with generating polynomials: x^25 + 2*x^24 + 2*x^23 + 2*x^22 + x^21 + 2*x^20 + x^18 + 2*x^17 + 2*x^16 + x^15 + 2*x^11 + 2*x^10 + 2*x^8 + x, x^23 + x^22 + 2*x^21 + x^19 + x^17 + x^15 + x^14 + 2*x^13 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + 1, x^25 + 2*x^24 + 2*x^23 + 2*x^22 + x^21 + x^20 + 2*x^19 + 2*x^17 + x^16 + x^12 + x^11 + 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + x^4 + 2*x^3 + x^2 + 2*x + 1, x^25 + x^23 + x^22 + x^21 + 2*x^17 + x^15 + x^12 + x^11 + 2*x^8 + 2*x^7 + 2*x^5 + 2*x^4 + 2*x^2 + x + 1, x^25 + x^23 + x^21 + x^20 + x^19 + x^17 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^6 + 2*x^3 + 2*x^2 + 2*x + 1, 2*x^23 + x^21 + x^18 + x^17 + 2*x^14 + 2*x^13 + 2*x^11 + 2*x^10 + 2*x^8 + x^7 + x^6 + x^5 + x^3 + x^2 + x, x^24 + x^23 + 2*x^21 + 2*x^20 + x^18 + 2*x^17 + x^16 + x^14 + x^12 + 2*x^11 + x^9 + 2*x^8 + x^5 + x^4 + 2*x^2 + x + 1, 2*x^24 + x^22 + 2*x^21 + x^20 + 2*x^19 + 2*x^17 + x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + x^11 + 2*x^10 + x^9 + x^6 + x^5 + x^4 + x^3 + 2*x + 1 [6]: [208, 7, 132] Quasicyclic of degree 8 Linear Code over GF(3) QuasiCyclicCode of length 208 with generating polynomials: 2*x^25 + 2*x^23 + x^22 + x^21 + x^20 + 2*x^19 + x^18 + 2*x^16 + x^15 + x^14 + 2*x^13 + x^9 + x^8 + x^6, 2*x^24 + 2*x^21 + 2*x^20 + x^19 + 2*x^17 + 2*x^15 + 2*x^13 + 2*x^12 + x^11 + x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2, 2*x^25 + 2*x^22 + 2*x^21 + 2*x^20 + 2*x^17 + x^16 + 2*x^15 + x^13 + x^12 + x^11 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x, x^25 + x^24 + x^23 + 2*x^22 + x^21 + x^20 + x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^14 + x^13 + 2*x^12 + 2*x^11 + x^10 + x^9 + 2*x^8 + 2*x^7 + 2*x^4 + 2*x, 2*x^25 + x^22 + x^20 + x^16 + x^14 + x^13 + 2*x^12 + x^11 + 2*x^10 + x^8 + 2*x^5 + x^3 + x^2 + 2*x + 2, x^24 + x^23 + x^22 + 2*x^21 + x^20 + x^18 + x^17 + x^14 + x^13 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + 2*x^6 + x^2, 2*x^25 + 2*x^24 + 2*x^22 + 2*x^21 + x^19 + x^18 + 2*x^16 + x^15 + 2*x^14 + 2*x^12 + 2*x^10 + x^9 + 2*x^7 + x^6 + 2*x^3 + 2*x^2 + 1, x^24 + 2*x^23 + 2*x^21 + x^20 + x^18 + 2*x^16 + x^14 + x^13 + x^11 + x^9 + x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 2 [7]: [208, 8, 130] Quasicyclic of degree 8 Linear Code over GF(3) The Vector space sum: [6] + [5] [8]: [212, 8, 134] Linear Code over GF(3) ConstructionXX using [7] [6] [5] [4] and [4] [9]: [213, 8, 135] Linear Code over GF(3) ConstructionX using [8] [3] and [1] last modified: 2008-11-06
Lb(213,8) = 132 is found by truncation of: Lb(216,8) = 135 BZ Ub(213,8) = 138 follows by a one-step Griesmer bound from: Ub(74,7) = 45 follows by a one-step Griesmer bound from: Ub(28,6) = 15 HHM
HHM: N. Hamada, T. Helleseth, H.M. Martinsen & Ø. Ytrehus, There is no ternary [28,6,16] code
Notes
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