lower bound: | 52 |
upper bound: | 58 |
Construction of a linear code [99,12,52] over GF(3): [1]: [101, 12, 54] 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, 0, 1, 1, 2, 0, 0, 1, 2, 0, 2, 2, 1, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 2, 2, 0, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 1, 2, 0, 1, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 1, 1, 2, 0, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 2, 1, 1, 2, 1, 1, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 0, 2, 1, 1, 2, 1, 2, 2, 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 0, 2, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 1, 2, 0, 0, 1, 2, 0, 1, 1, 2, 0, 0, 2, 1, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 0, 1, 2, 0, 2, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 1, 2, 1, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 1, 2, 0, 1, 2, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 0, 1, 1, 2, 1, 0, 1, 2, 2, 0, 2, 1, 2, 1, 2, 0, 0, 2, 1, 2, 1, 0, 2, 1, 0, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 1, 0, 2, 0, 1, 2, 2, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 2, 2, 0, 0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 0, 0, 1, 2, 0, 2, 0, 0, 1, 2, 1, 1, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 2, 0, 1, 0, 2, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 1, 2, 2, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 1, 2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 0, 1, 1, 1, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 0, 0, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 2, 0, 1, 0, 1, 0, 1, 2, 2, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 2, 2, 2, 2, 1, 0, 1, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 1, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 1, 1, 0, 1, 0, 1, 2, 2, 1, 1, 1, 2, 1, 0, 1, 2, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 2, 2, 1, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 2, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 1, 0, 0, 1, 2, 0, 2, 2, 2, 1, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 1, 1, 0, 0, 0, 1, 2, 1, 2, 1, 1, 0, 2, 2, 0, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 0, 0, 1, 2, 1, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2 ] [ 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, 1, 1, 1, 1, 0, 0, 0, 0, 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, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 0 ] [2]: [99, 12, 52] Linear Code over GF(3) Puncturing of [1] at { 100 .. 101 } last modified: 2010-01-04
Lb(99,12) = 51 is found by taking a subcode of: Lb(99,13) = 51 is found by shortening of: Lb(101,15) = 51 XX Ub(99,12) = 58 is found by considering shortening to: Ub(98,11) = 58 BKn
XX:
Notes
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