lower bound: | 22 |
upper bound: | 24 |
Construction of a linear code [45,10,22] over GF(3): [1]: [47, 10, 24] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1, 2, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 0, 1, 2, 1, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 1, 1, 1, 1, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 0, 1, 2, 1, 0, 0, 0, 2, 2, 1, 2, 1, 1, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2, 0, 2, 0, 1, 1, 1, 2, 2, 0, 2, 1, 0, 0, 0, 1, 2, 1, 0, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 1, 1, 1, 2, 1, 2, 1, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 2, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 2, 1, 1, 2, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 1, 2, 1, 1, 1, 1, 1, 2, 0, 0, 1, 2, 1, 2 ] [2]: [45, 10, 22] Linear Code over GF(3) Puncturing of [1] at { 46 .. 47 } last modified: 2010-02-16
Lb(45,10) = 21 is found by taking a subcode of: Lb(45,11) = 21 is found by shortening of: Lb(46,12) = 21 DaH Ub(45,10) = 24 follows by a one-step Griesmer bound from: Ub(20,9) = 8 is found by considering shortening to: Ub(17,6) = 8 is found by considering truncation to: Ub(16,6) = 7 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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