lower bound: | 33 |
upper bound: | 37 |
Construction of a linear code [66,11,33] over GF(3): [1]: [69, 11, 36] Quasicyclic of degree 3 Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 0, 2, 2, 2, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 1, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0, 1, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 2, 2, 2, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 2, 2, 2, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 2, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 1, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 0, 2, 2, 0, 1, 0, 1, 1, 2, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 1, 2, 2, 0, 1, 2, 0, 0, 2, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 0, 2, 2, 0, 1, 0, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 2, 2, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 2, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 2, 0, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 0, 2, 1, 2, 1, 0, 0, 1, 1, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 2, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1 ] [2]: [66, 11, 33] Linear Code over GF(3) Puncturing of [1] at { 67 .. 69 } last modified: 2001-12-17
Lb(66,11) = 33 is found by taking a subcode of: Lb(66,12) = 33 DaH Ub(66,11) = 37 follows by a one-step Griesmer bound from: Ub(28,10) = 12 follows by a one-step Griesmer bound from: Ub(15,9) = 4 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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