lower bound: | 54 |
upper bound: | 54 |
Construction of a linear code [90,9,54] over GF(3): [1]: [90, 9, 54] Linear Code over GF(3) code found by Tatsuya Maruta Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 0, 0, 1, 0, 2, 1, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 1, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0, 1, 0, 0, 2, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 0, 0, 1, 0, 2, 1, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 1, 1, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0, 1, 0, 1, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 0, 0, 1, 0, 0, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2, 2, 1, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 0, 2, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 0, 0, 1, 0, 0, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2, 2, 1, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 0, 2, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 1, 1, 0, 2, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 1, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 2, 2, 0, 1, 1, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 1, 2, 2, 0, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 1, 1, 2, 2, 1, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 0, 0, 1, 0, 2, 1, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 1, 1, 2 ] last modified: 2006-10-04
Lb(90,9) = 54 MST Ub(90,9) = 54 follows by a one-step Griesmer bound from: Ub(35,8) = 18 follows by a one-step Griesmer bound from: Ub(16,7) = 6 vE2
vE2: M. van Eupen, Four nonexistence results for ternary linear codes, IEEE Trans. Inform. Theory 41 (1995) 800-805.
Notes
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