lower bound: | 131 |
upper bound: | 133 |
Construction of a linear code [204,7,131] over GF(3): [1]: [121, 116, 3] "Hamming code (r = 5)" Linear Code over GF(3) 5-th order HammingCode over GF( 3) [2]: [121, 5, 81] Cyclic Linear Code over GF(3) Dual of [1] [3]: [119, 5, 79] Linear Code over GF(3) Puncturing of [2] at { 120 .. 121 } [4]: [40, 4, 27] Linear Code over GF(3) ResidueCode of [3] [5]: [38, 4, 25] Linear Code over GF(3) Puncturing of [4] at { 39 .. 40 } [6]: [13, 3, 9] Linear Code over GF(3) ResidueCode of [5] [7]: [11, 3, 7] Linear Code over GF(3) Puncturing of [6] at { 12 .. 13 } [8]: [4, 2, 3] Linear Code over GF(3) ResidueCode of [7] [9]: [200, 5, 131] Quasicyclic of degree 25 Linear Code over GF(3) QuasiCyclicCode of length 200 with generating polynomials: 2*x^7 + x^6 + 2*x^5 + 1, x^7 + x^5 + x^4 + 2*x^3 + 2*x + 2, x^6 + x^4 + 2*x^3 + 2*x, 2*x^7 + 2*x^5 + x^2 + 1, 2*x^7 + x^6 + x^5 + x + 1, x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + 1, x^6 + 2*x^5 + x^4 + 2*x^3, x^7 + x^6 + 2*x^4 + x^2 + x, x^7 + x^6 + x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2, x^7 + x^6 + 2*x^4 + x^3 + 2*x + 2, x^7 + x^6 + x^5 + x^2 + 2, x^7 + 2*x^6 + x^5 + 2, x^7 + x^6 + 2*x^5 + x^2 + 2*x + 2, 2*x^7 + x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x^2 + x + 1, x^6 + 2*x^3 + 2*x + 1, 2*x^7 + 2*x^6 + x^5 + 2*x^3 + 2, 2*x^7 + x^3, 2*x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + x^2, 2*x^7 + 2*x^6 + 2*x^5 + 2*x^3 + 2*x + 2, 2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^2 + x, x^7 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x, x^6 + 2*x^5 + x^4 + 2*x^2 + x + 2, x^7 + x^6 + x^2 + x + 2, x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2 [10]: [200, 7, 128] Quasicyclic of degree 25 Linear Code over GF(3) QuasiCyclicCode of length 200 with generating polynomials: 2*x^7 + 1, x^5 + x^4 + x^3 + 2*x^2 + x, x^6 + 2*x^3, 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x + 1, 2*x^7 + x^6 + 2*x^5 + 2*x^4 + x^3 + x^2, 2*x^6 + 2*x^3 + 2*x^2 + x + 2, 2*x^6 + 2*x^5 + 2*x^4 + x^2 + 2, 2*x^7 + x^6 + x^5 + x^4 + 2*x^3 + 2*x, 2*x^7 + x^6 + 2*x^5 + 2*x^2 + 2*x, x^6 + 2*x^5 + x^4 + x^3 + x^2 + 2*x + 1, x^7 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 1, x^5 + 2*x^3 + x^2 + x + 1, 2*x^7 + x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1, 2*x^6 + 2*x^5 + x^4 + x^3 + x + 2, 2*x^6 + 2*x^5 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^7 + x^6 + x^5 + 2*x^4 + x^3 + x^2 + x, 2*x^7 + 2*x^5 + 2, 2*x^7 + x^5, 2*x^7 + 2*x^6 + 2*x^5 + x^2 + 2, 2*x^7 + 2*x^6 + x^4 + 2*x^3 + 2*x^2, 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^3, x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 2, 2*x^7 + x^6 + 2*x^2 + x, x^6 + 2*x^4 + 2*x^2 + x, x^7 + 2*x^6 + x^5 + x^3 + 2*x + 2 [11]: [204, 7, 131] Linear Code over GF(3) ConstructionX using [10] [9] and [8] last modified: 2003-10-08
Lb(204,7) = 131 GW2 Ub(204,7) = 133 follows by a one-step Griesmer bound from: Ub(70,6) = 44 is found by considering truncation to: Ub(69,6) = 43 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
|