lower bound: | 127 |
upper bound: | 132 |
Construction of a linear code [204,8,127] over GF(3): [1]: [205, 8, 128] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 2, 0, 2, 1, 1, 2, 0, 1, 0, 1, 2, 2, 1, 2, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 2, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 1, 1, 1, 0, 2, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 0, 1, 1, 1, 2, 0, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 2, 2, 0, 2, 0, 1, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 0, 2, 1, 2, 1, 0, 1, 2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 1, 2, 1, 2, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2, 1, 1, 2, 0, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 2, 0, 1, 2, 2, 2, 2, 0, 0, 1, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 2, 2, 0, 1, 2, 1, 2, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 2, 1, 1, 0, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 0, 1, 0, 2, 0, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 1, 2, 0, 2, 1, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 2, 1, 0, 0, 2, 2, 2, 1, 1, 2, 1, 0, 2, 0, 2, 2, 1, 1, 2, 0, 1, 2, 2, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 0, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 0, 2, 0, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2, 1, 1, 2, 1, 0, 2, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 0, 2, 0, 1, 0, 0, 2, 1, 0, 2, 1, 1, 0, 1, 1, 1, 2, 2, 0, 1, 2, 1, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 0, 1, 1, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 0, 1, 0, 1, 0, 2, 1, 2, 2, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 1, 2, 1, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 1, 0, 1, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 2, 2, 2, 1, 1, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 1, 1, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 1, 2, 1, 1, 2, 1, 2, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 1, 1, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 1, 2, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 2, 1, 1, 2, 0, 2, 0, 2, 2, 0, 2, 1, 2, 1, 1, 1, 2, 2, 0, 0, 0, 1, 2, 0, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 0, 1, 1, 1, 2, 2, 0, 0, 0, 2, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 1, 2, 1, 1, 1, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 2, 0, 1, 0, 2, 2, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 2, 1, 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 0, 1, 0, 1, 2, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 1, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 0, 2, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 1, 1, 2, 2, 2, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 1, 2, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 1, 2, 2, 1, 2, 1, 0, 2, 1, 2, 0, 2, 2, 0, 0, 1, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 2, 1, 1, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 2, 2, 1, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 1, 2, 2, 2, 1, 2, 0, 2, 0, 0, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 2, 2, 1, 0, 2, 2, 0, 2, 0, 1, 2, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 1, 2, 0, 0, 1, 0, 2, 2, 1, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] [2]: [204, 8, 127] Linear Code over GF(3) Puncturing of [1] at { 205 } last modified: 2005-04-07
Lb(204,8) = 127 is found by truncation of: Lb(205,8) = 128 BKW Ub(204,8) = 132 follows by a one-step Griesmer bound from: Ub(71,7) = 44 is found by considering shortening to: 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
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