lower bound: | 126 |
upper bound: | 130 |
Construction of a linear code [201,8,126] over GF(3): [1]: [200, 8, 126] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 2, 2, 0, 1, 1, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 0, 2, 0, 1, 1, 1, 2, 2, 0, 2, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 2, 1, 2, 1, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 1, 2, 1, 1, 2, 1, 0, 1, 0, 2, 1, 2, 2, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 1, 0, 1, 2, 1, 2, 0, 2, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 1, 2, 0, 2, 0, 1, 2, 1, 2, 2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 2, 2, 1, 1, 1, 0, 2, 0, 1, 1, 0, 2, 0, 2, 1, 2, 2, 2, 2, 1, 2, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 1, 1, 1, 2, 2, 2, 0, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 1, 1, 2, 0, 1, 0, 0, 1, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 1, 1, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 0, 2, 0, 1, 0, 1, 1, 2, 1, 0, 2, 0, 1, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 0, 2, 0, 0, 0, 1, 2, 1, 1, 0, 2, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 1, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 0, 1, 2, 2, 1, 0, 2, 1, 2, 0, 1, 2, 2, 0, 2, 1, 0, 2, 2, 2, 1, 0, 0, 1, 0, 1, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 2, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 2, 2, 1, 2, 2, 1, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 2, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 2, 1, 0, 0, 0, 1, 2, 0, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 2, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 2, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 1, 0, 2, 2, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 0, 2, 1, 0, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 0, 2, 0, 1, 1, 1, 2, 2, 0, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 2, 1, 2, 0, 0, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 2, 0, 1, 2, 1, 0, 0, 1, 1, 0, 2, 2, 1, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 2, 0, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 1, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 1, 1, 2, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 2, 0, 1, 2, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 1, 1, 0, 2, 2, 0, 2, 1, 2, 0, 1, 1, 2, 1, 1, 2, 2, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0, 1, 2, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 2, 0, 0, 2, 2, 1, 0, 1, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 2, 0, 0, 2, 1, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 0, 1, 2, 0, 2, 0, 1, 0, 0, 2, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2, 2, 2, 0, 1, 1, 1 ] [ 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, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1 ] [2]: [201, 8, 126] Linear Code over GF(3) ExtendCode [1] by 1 last modified: 2005-04-07
Lb(201,8) = 126 is found by lengthening of: Lb(200,8) = 126 BKW Ub(201,8) = 130 follows by a one-step Griesmer bound from: Ub(70,7) = 43 is found by considering shortening 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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