lower bound: | 153 |
upper bound: | 155 |
Construction of a linear code [237,7,153] over GF(3): [1]: [2, 1, 2] Cyclic Linear Code over GF(3) RepetitionCode of length 2 [2]: [234, 6, 153] Quasicyclic of degree 18 Linear Code over GF(3) QuasiCyclicCode of length 234 with generating polynomials: 2*x^11 + x^9 + 2*x^8 + x^7 + 2*x^6 + 1, 2*x^12 + 2*x^10 + x^6 + x^5 + 2*x^3 + 1, x^11 + x^10 + x^7 + 2*x^6 + 2*x^2 + 2, 2*x^11 + x^10 + 2*x^8 + 2*x^7 + 2*x^6 + x^5 + 2*x^2 + 2*x + 1, x^11 + x^10 + x^9 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x, 2*x^10 + x^7 + x^4 + x^2 + 2*x + 2, 2*x^12 + x^11 + x^8 + 2*x^7 + 2*x^6 + x^4 + 2*x^3 + 2*x^2 + 2, x^11 + x^9 + x^8 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 2*x, 2*x^12 + x^11 + 2*x^9 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + x + 2, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + x^2 + 2, x^12 + x^11 + 2*x^10 + x^9 + x^8 + x^3 + 2*x^2 + 2*x + 1, 2*x^10 + x^8 + 2*x^6 + x^5 + 2*x^4 + x^3, 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^6 + 2*x^5 + 2*x^3 + 2*x + 2, x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^7 + 2*x^4 + x^3 + 2*x^2 + 1, x^12 + x^11 + 2*x^10 + x^9 + 2*x^8 + 2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2, 2*x^11 + 2*x^10 + 2*x^9 + x^8 + 2*x^5 + 2*x^4 + x^3 + 2*x + 1, x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 2*x^2 + 2, 2*x^12 + 2*x^10 + x^9 + x^8 + 2*x^7 + 2*x^5 + 2*x^3 + 2*x + 1 [3]: [234, 7, 151] Quasicyclic of degree 18 Linear Code over GF(3) QuasiCyclicCode of length 234 with generating polynomials: x^12 + x^9 + x^7 + 1, x^12 + x^11 + x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + x + 2, 2*x^12 + x^10 + x^9 + x^8 + 2*x^7 + x^6 + x^5 + x^4 + x^3 + 2, x^12 + x^10 + x^9 + 2*x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 1, 2*x^12 + x^10 + 2*x^9 + 2*x^8 + x^7 + 2*x^5 + x^4 + x^3 + 2*x + 2, 2*x^10 + 2*x^9 + 2*x^8 + x^4 + x^3 + 2*x^2 + x, x^11 + x^10 + x^9 + 2*x^8 + x^7 + x^4 + 2*x^2 + 2*x + 1, x^12 + 2*x^11 + 2*x^10 + x^8 + x^6 + x^5 + 2*x^4 + 2*x^2 + x + 1, x^11 + x^10 + 2*x^5 + 2*x^3 + x^2 + 2*x + 1, 2*x^10 + x^9 + 2*x^7 + 2*x^5 + x^2 + x, x^12 + 2*x^11 + x^10 + 2*x^9 + x^3 + 2*x, 2*x^12 + 2*x^11 + x^10 + x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^12 + x^11 + 2*x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^3 + 2*x^2 + x, 2*x^11 + x^10 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + x + 2, x^11 + x^9 + 2*x^7 + x^6 + 2*x^5 + 2*x^3 + 2, 2*x^11 + x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x, 2*x^11 + x^10 + 2*x^8 + x^6 + 2*x^5 + x^3 + 2, x^12 + x^11 + x^9 + 2*x^8 + x^7 + x^6 + 2*x^3 + 2*x^2 + x + 2 [4]: [236, 7, 153] Linear Code over GF(3) ConstructionX using [3] [2] and [1] [5]: [237, 7, 153] Linear Code over GF(3) ExtendCode [4] by 1 last modified: 2008-05-17
Lb(237,7) = 153 is found by lengthening of: Lb(236,7) = 153 GW2 Ub(237,7) = 155 follows by a one-step Griesmer bound from: Ub(81,6) = 51 Ma
Ma: T. Maruta, On the nonexistence of linear codes attaining the Griesmer bound, Geom. Dedicata 60 (1996) 1-7. T. Maruta, On the nonexistence of linear codes of dimension four attaining the Griesmer bound, pp. 117-120 in: Optimal codes and related topics, Proc. Workshop Sozopol, Bulgaria, 1995. T. Maruta, The nonexistence of [116,5,85]_4 codes and [187,5,139]_4 codes, Proc. 2nd International Workshop on Optimal Codes and Related Topics in Sozopol (1998), pp. 168-174. T. Maruta & M. Fukui, On the nonexistence of some linear codes of dimension 4 over GF(5), preprint, 1995. T. Maruta, M. Takenaka, M. Shinohara, K. Masuda & S. Kawashima, Constructing new linear codes over small fields, preprint 2004.
Notes
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