lower bound: | 109 |
upper bound: | 114 |
Construction of a linear code [180,9,109] over GF(3): [1]: [181, 9, 110] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 1, 0, 2, 1, 2, 2, 1, 2, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 2, 1, 2, 2, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 1, 2, 2, 0, 2, 1, 2, 0, 0, 0, 1, 2, 2, 1, 1, 2, 1, 1, 0, 0, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 2, 0, 1, 0, 2, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 2, 0, 0, 2, 1, 2, 0, 0, 1, 2, 2, 0, 0, 2, 0, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 0, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 1, 0, 2, 1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 0, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 1, 0, 2, 2, 1, 2, 2, 0, 1, 1, 2, 2, 1, 2, 0, 1, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 1, 1, 2, 1, 1, 2, 0, 2, 1, 1, 1, 1, 1, 0, 2, 0, 1, 0, 2, 2, 1, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 2, 0, 1, 0, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 1, 0, 2, 1, 1, 2, 2, 2, 2, 0, 1, 2, 2, 2, 0, 2, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 1, 2, 1, 1, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2, 0, 1, 0, 1, 2, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 2, 2, 0, 1, 2, 1, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 1, 1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 1, 2, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 2, 0, 0, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 2, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 1, 1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 1, 0, 2, 2, 1, 1, 0, 2, 0, 0, 2, 1, 0, 2, 0, 0, 2, 1, 1, 1, 2, 0, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 1, 0, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2, 2, 2, 2, 1, 1, 0, 1, 0, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 1, 0, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2, 2, 2, 2, 1, 1, 0, 1, 0, 2, 1, 1, 2, 2, 2, 1, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 2, 0, 1, 0, 0, 2, 1, 2, 0, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2, 1, 1, 2, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 0, 1, 0, 2, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 1, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 1, 0, 2, 1, 0, 2, 0, 1, 0, 2, 2, 0, 1, 2, 2, 0, 1, 1, 2, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 2, 2, 0, 1, 0, 2, 0, 1, 0, 1, 1, 2, 1, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 2, 2, 2, 0, 0, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 1, 2, 2, 1, 2, 2, 0, 0, 1, 2, 1, 0, 1, 2, 0, 2, 2, 2, 0, 1, 2, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 1, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 2 ] [2]: [180, 9, 109] Linear Code over GF(3) Puncturing of [1] at { 181 } last modified: 2003-11-25
Lb(180,9) = 108 is found by lengthening of: Lb(178,9) = 108 MST Ub(180,9) = 114 is found by considering truncation to: Ub(179,9) = 113 Gur
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
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