lower bound: | 54 |
upper bound: | 57 |
Construction of a linear code [96,11,54] over GF(3): [1]: [95, 11, 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, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 1, 0, 2, 2, 0, 1, 0, 1, 0, 2, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 1, 0, 2, 2, 0, 1, 0, 1, 1, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 0, 0, 1, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 2, 1, 1, 0, 2, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 0, 1, 0, 0, 2, 1, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 0, 1, 2, 0, 1, 0, 1, 0, 2, 2, 0, 2, 1 ] [2]: [96, 11, 54] Linear Code over GF(3) ExtendCode [1] by 1 last modified: 2006-10-04
Lb(96,11) = 54 is found by lengthening of: Lb(95,11) = 54 MST Ub(96,11) = 57 follows by a one-step Griesmer bound from: Ub(38,10) = 19 follows by a one-step Griesmer bound from: Ub(18,9) = 6 is found by considering shortening to: 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
|