lower bound: | 169 |
upper bound: | 173 |
Construction of a linear code [236,7,169] over GF(4): [1]: [240, 7, 173] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, w, w, 0, 1, 0, w, 0, 1, w, 1, 0, 0, w, 1, w, 0, w^2, w^2, 1, 0, 0, w^2, w, 0, w^2, 1, 0, w^2, w, 0, w, 0, 0, 0, w, 0, w^2, w^2, w, 1, 0, 0, 0, w^2, 0, w^2, 0, 0, w^2, w, w, w^2, 0, 0, 0, w, w, 1, 1, 1, 1, w^2, 0, w^2, 1, w^2, 0, w, 1, 1, w^2, w, w, w, w^2, w^2, 0, 1, 0, w, w^2, w^2, 1, w, w, w, 1, w, 1, 1, 1, 1, 0, w, w, 0, 1, w^2, w, w^2, w^2, 0, 1, w, w, 1, w, 0, 0, 0, w^2, w, w, w, 0, 1, w^2, 1, w^2, 0, w, w^2, 1, 1, w^2, w^2, 0, 1, w, w^2, 1, w^2, w^2, w^2, 1, w, 1, 0, w, w, w^2, 0, 1, w, w^2, w^2, w^2, 1, w, 0, w^2, 1, w, 1, w, 0, w^2, 1, 0, 1, w^2, w, w, w, 1, w^2, w, 0, 1, 0, 1, w, w, w, 1, w^2, 1, 0, w, w, w^2, 1, 1, 0, w^2, 0, w, w, 1, w, 0, w, 0, 1, w^2, w^2, 0, w, 0, 0, 1, 0, 1, 1, w, w, 1, w^2, w^2, 0, w, 1, 0, w, 0, 1, w^2, 1, 1, w^2, 0, 1, w, 1, w, 1, 1, 0, 1, w^2, w^2, 1, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, w^2, 1, w, w, 1, w^2, w, w, 1, 0, 1, 0, w^2, 0, w, 0, 1, w, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, w, w^2, w, 0, 0, w^2, w, 1, w, 0, 0, 1, 0, 0, 1, w^2, 1, w^2, 0, 1, 0, 1, w^2, w^2, 0, 0, w^2, 1, 0, w^2, w^2, w^2, 0, w^2, 1, 1, 0, w^2, w^2, 0, w^2, 0, 0, 1, 1, w^2, w, w^2, w, 1, w^2, w^2, w, 1, w, 1, 1, 0, w, 0, w^2, w^2, w^2, w, w^2, 1, w, w, 0, 0, w^2, w, w^2, w, w, 1, 0, w, w, 0, 0, 1, 0, 1, 1, w, w, 0, 1, 0, w^2, w^2, w^2, 1, w^2, 0, w, w^2, w, w, w^2, 1, 0, w, w, 1, w, 0, 1, w^2, 1, w^2, w^2, w, w, w^2, w, w, 1, w, 0, 1, w^2, w, 0, w, w, 1, 1, 1, w, 0, 0, 1, 1, 0, 0, 0, w, w, 1, w, w, 1, 1, 0, 0, 1, 1, w^2, 1, w^2, 1, w^2, 1, 1, w^2, w^2, 1, 0, w, w, w^2, w, w, 0, w, w^2, w^2, w, 0, w, 1, w, 0, w, 1, 0, 0, w, 1, w^2, 0, 1, w^2, w, w, 0, 1, w^2, 0, w^2, w, w, 0, w, 0, w^2, 1, w, 0, w, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, w^2, 0, 1, 0, w, w, w^2, 0, 1, w^2, 0, 1, w^2, 1, w^2, w, 1, 0, 0, 1, 1, 1, w, 0, 0, w^2, 1, 0, w, 0, 1, w^2, w, 0, w^2, w^2, w^2, 0, 1, w, 0, 1, 0, 1, 1, w, 1, w^2, 1, w, w^2, 0, w^2, w^2, 0, w^2, 0, w^2, w, 1, 1, w, 0, w, w^2, 0, 0, 0, 1, w, w, w^2, w^2, w, 0, w, w, 1, w, w, w, w, 0, w, 1, w, w^2, w^2, 0, w, 1, 1, w, 1, 0, 1, 0, w^2, w^2, 1, w, w, 1, 1, 1, w^2, w^2, w, w, 0, 1, w, w^2, w, 1, 0, w^2, w, 0, 0, 0, w, 1, w^2, w, 1, w, 1, 1, w^2, 1, 0, 1, w^2, 0, w, 0, 0, w, 0, 0, w^2, 1, 1, w^2, w, w^2, 0, w, w, 1, w^2, 0, 0, w^2, w, w^2, w^2, 1, w^2, w^2, w^2, w^2, w, w^2, 1, w^2, 0, 0, w, w^2, 1, 1, w, w^2, 1, w, 1, w, 0, 0, 1, w^2, w^2, 1, 1, 0, 0, w^2, w^2, w, 1, w^2, 0, w^2, 1, w, 0, w^2, w, w, w, w^2, 0, w^2, 1, w^2, 1, 1, 1, w, 1, 0, w, w^2, w, w^2, w, w^2, w, 0, 1, 1, 0, w^2, 0, w, w^2, w^2, w^2, 1, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 1, w, 0, w, 0, w^2, w, 0, 0, w, w^2, 0, 0, 0, 0, w, 0, w^2, w^2, 0, 1, w^2, 0, w, w, w^2, w^2, w^2, 1, w, 1, 1, w^2, w, 1, w^2, 1, 1, 1, w, w, 0, 1, w, 1, w^2, w, 1, 1, 0, w^2, 1, 0, w^2, w^2, 1, w, w^2, 0, 1, w, w^2, w, w, 1, 1, 0, 1, w^2, w, 0, w^2, w, w, 0, w, w, 1, 1, w^2, 0, 0, 1, 1, w^2, 0, 1, w, 0, w^2, 1, w, 0, w^2, 0, 0, w, w, w, 1, w^2, w, 1, 0, 0, w, w, w^2, w, w, w, 0, w^2, w, w, w, w, 0, 0, 0, 1, w, 1, w, 1, 0, 1, 1, 0, w^2, 0, w^2, w, w^2, 0, 1, 1, 0, 1, w^2, 0, 0, 0, 0, w^2, 1, 0, 0, 1, w, 0, 0, w, w^2, 1, w^2, 0, 0, w^2, w, 1, w, w, w, 1, 1, 0, w^2, w^2, 0, 1, w, 0, 0, 1, 1, w, w, 0, w^2, w, w^2, w, w^2, w^2, 1, 0, 1, w^2, w, w^2, w^2, 1, 0, w, 1, 1, w^2, 0, w^2, 1, w, 1, w, 1, w, w, 1, w^2, 0, 0, 1, 1, 1, w, 1, 0, 0, 1, 1, w, w^2, 0, w, 1, 0, w^2, w, 0, 1, 1, w, w ] [ 0, 0, 0, 0, 1, 0, 0, w, w^2, w, 1, w, w, w^2, w^2, w^2, 1, w, w^2, w, 1, w, w^2, 1, w^2, w, w^2, 0, w, 1, 1, 1, w^2, w^2, 0, 1, 1, 0, 1, 1, w^2, 0, 1, 0, w, w^2, 0, w, w, 0, w, w, w, w^2, w, w, w^2, w, 0, 1, 0, w^2, 1, w^2, w^2, w, 1, 0, 1, w^2, 1, w^2, w, 1, w, 0, w, 1, w, 1, 0, 1, w^2, w, w^2, 1, w^2, 0, w^2, 1, w^2, w^2, 1, 1, w^2, w^2, 1, w, 0, 0, w, 1, 0, 1, 1, 0, 1, w, w^2, w^2, w^2, w, 1, 0, w, w^2, w, 1, 0, w, 1, w, w^2, 1, w^2, w^2, 0, w, w, w^2, 0, 1, w, 0, 0, w^2, w^2, w, w^2, 0, 1, w, w, 0, 1, w, w^2, w, 0, 1, w, w^2, 0, w, 1, w, w, 1, w^2, w, w^2, 1, 1, 0, 1, 0, w, 1, w^2, 0, 0, w^2, w, w^2, 0, w, w^2, 1, w^2, 0, w, 1, w, 0, w, 0, w, 0, w^2, w, w, 0, w^2, w^2, w, 0, 1, w, 1, w^2, 0, w^2, 1, 1, w^2, w^2, 0, w, 1, w^2, w^2, 0, w^2, w^2, 1, w, w, w, 1, 1, w^2, 1, w, w, 1, 1, w, 1, w^2, 1, 1, 0, 0, 1, w^2, w^2, w^2, w, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 1, w^2, w^2, 1, 1, w^2, w, 0, w^2, 0, 1, w, w, 1, 0, 0, 1, w^2, 0, w, w^2, w, w^2, 1, w^2, w, w^2, 1, 1, 1, 0, 0, 1, 1, w, 0, w^2, w, w^2, 0, 0, w, w, w, w, 0, w, w^2, 0, w^2, w, 0, 0, 1, 0, w, 0, 0, 0, 1, w, w, 1, 1, w, 1, w, 0, 1, w^2, 0, 0, w^2, 0, w, w^2, w^2, 1, w^2, 0, 1, w, 0, 0, w, w, w, 0, 0, 0, w, 1, 0, 1, w^2, 1, w^2, w^2, 0, w, w^2, w, 0, w, w, 1, 0, 0, w, w^2, 0, 0, 1, w^2, 1, 1, 1, w, 1, w^2, 1, 0, 1, 0, w, w^2, w, w^2, 1, 1, 0, 0, 1, w, w, w^2, 1, 0, 0, w^2, w^2, w, w^2, 0, 0, 1, w, 1, 0, 1, 0, w, w, 1, w, 1, w^2, w^2, 1, w^2, 0, 0, w, 1, w^2, 1, w^2, w^2, w^2, w, 0, 0, w, 1, 1, w^2, 1, 0, w^2, 1, 0, w^2, 0, w, 1, 0, w, w, 1, 1, 1, w^2, 1, 0, w, 1, 1, 0, w^2, w^2, w^2, w, w, 0, w, 1, 0, 1, w^2, w, w^2, 1, 1, 0, w^2, 1, 0, 1, w, w^2, w, w, w, w, 0, w^2, w^2, 1, 0, 1, 1, 1, w ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, w^2, 0, 1, 0, w^2, 1, w^2, 0, 0, 1, w^2, 1, 0, w, w, w^2, 0, 0, w, 1, w^2, w, w^2, 0, w, 1, 0, 1, 0, 0, 0, 1, 0, w, w, 1, w^2, 0, 0, 0, w, 0, w, 0, 0, w, 1, 1, w, 0, 0, 0, 1, 1, w^2, w^2, w^2, w^2, w, 0, w, w^2, w, 0, 1, w^2, w^2, w, 1, 1, 1, w, w, 0, w^2, 0, 1, w, w, w^2, 1, 1, 1, w^2, 1, w^2, w^2, w^2, w^2, 1, 1, 1, 0, w^2, w, 1, w, w, 0, w^2, 1, 1, w^2, 1, 0, 0, 0, w, 1, 1, 1, 0, w^2, w, w^2, w, 0, 1, w, w^2, w^2, w, w, 0, w^2, 1, w, w^2, w, w, w, w^2, 1, w^2, 0, 1, 1, 1, 0, w^2, 1, w, w, w, w^2, 1, 0, w, w^2, 1, w^2, 1, 0, w, w^2, 0, w^2, w, 1, 1, 1, w^2, w, 1, 0, w^2, 0, w^2, 1, 1, 1, w^2, w, w^2, 0, 1, 1, w, w^2, w^2, 0, 0, 0, 1, 1, w^2, 1, 0, 1, 0, w^2, w, w, 0, 1, 0, 0, w^2, 0, w^2, 1, 1, 1, w^2, w, w, w^2, 1, w^2, 0, 1, 0, 0, w, w^2, w^2, w, 0, w^2, 1, w^2, 1, w^2, w^2, 0, w^2, w, w, w^2, w, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [236, 7, 169] Linear Code over GF(2^2) Puncturing of [1] at { 237 .. 240 } last modified: 2002-10-15
Lb(236,7) = 169 is found by truncation of: Lb(237,7) = 170 Ma Ub(236,7) = 173 follows by a one-step Griesmer bound from: Ub(62,6) = 43 follows by a one-step Griesmer bound from: Ub(18,5) = 10 Liz
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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