lower bound: | 154 |
upper bound: | 157 |
Construction of a linear code [240,7,154] over GF(3): [1]: [240, 7, 154] Quasicyclic of degree 20 Linear Code over GF(3) QuasiCyclicCode of length 240 with generating polynomials: x^10 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + x + 2, 2*x^10 + x^9 + 2*x^8 + x^7 + 2*x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^10 + x^9 + 2*x^7 + x^5 + x^4 + x^3 + x^2 + x + 2, 2*x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 2, 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + 2*x^3 + x^2 + 2*x + 2, 2*x^10 + x^9 + x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + 2*x^2 + x + 2, x^10 + 2*x^9 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x + 2, 2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + 2*x + 2, x^10 + 2*x^9 + x^8 + x^7 + 2*x^5 + 2*x^3 + 2*x^2 + 2*x + 2, x^8 + 2*x^7 + x^6 + x^5 + x^3 + 2*x^2 + 2*x + 2, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x + 2, x^9 + x^8 + x^7 + 2*x^5 + 2*x^3 + 2, x^10 + 2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^4 + x^3 + x^2 + 2*x + 2, x^10 + 2*x^9 + x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x + 2, x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + x + 2, x^9 + x^8 + x^7 + 2*x^6 + x^5 + 2*x^3 + x^2 + x + 2, x^9 + 2*x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x + 2, x^10 + 2*x^9 + x^8 + 2*x^7 + x^6 + 2*x^5 + x^3 + x^2 + 2*x + 2, 2*x^9 + 2*x^7 + x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + 2*x + 2, x^9 + x^8 + 2*x^7 + x^6 + 2*x^5 + x^3 + 2*x^2 + 2 last modified: 2003-10-02
Lb(240,7) = 154 GO Ub(240,7) = 157 follows by a one-step Griesmer bound from: Ub(82,6) = 52 is found by considering truncation to: 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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