lower bound: | 84 |
upper bound: | 84 |
Construction of a linear code [116,5,84] over GF(4): [1]: [117, 6, 84] Quasicyclic of degree 9 Linear Code over GF(2^2) QuasiCyclicCode of length 117 with generating polynomials: w^2*x^12 + w*x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + w^2*x^7 + x^6 + 1, x^11 + w^2*x^9 + w*x^8 + w*x^6 + w^2*x^5 + x^3 + x + 1, x^12 + x^10 + x^7 + w*x^6 + w*x^5 + w*x^4 + w*x^3 + x^2, x^12 + x^11 + w^2*x^10 + x^8 + x^7 + x^6 + w*x^5 + x^3 + w*x^2 + w^2*x, w^2*x^12 + x^11 + x^10 + x^9 + w^2*x^7 + w*x^5 + w*x^4 + x^2 + w^2*x + w^2, x^12 + x^10 + x^9 + w*x^8 + w^2*x^7 + x^6 + w^2*x^5 + x^4 + x^3 + w*x^2 + w^2*x + w^2, x^12 + w^2*x^11 + w^2*x^10 + w*x^9 + w^2*x^8 + w*x^7 + x^6 + w^2*x^5 + w^2*x^4 + w^2*x^2 + w*x + w, w*x^12 + w*x^11 + x^9 + w^2*x^8 + w*x^7 + w^2*x^5 + w*x^4 + w*x^3 + w*x^2 + 1, x^11 + w*x^9 + w*x^8 + w*x^7 + x^6 + x^5 + x^4 + w*x^3 + w^2*x + w^2 [2]: [116, 5, 84] Linear Code over GF(2^2) Shortening of [1] at { 117 } last modified: 2002-10-16
Lb(116,5) = 84 is found by shortening of: Lb(117,6) = 84 Bou Ub(116,5) = 84 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.
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