lower bound: | 65 |
upper bound: | 69 |
Construction of a linear code [111,9,65] over GF(3): [1]: [112, 9, 66] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 1, 0, 1, 2, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, 0, 2, 1, 0, 2, 2, 1, 0, 2, 0, 1, 0, 1, 2, 0, 2, 2, 2, 1, 2, 0, 2, 1, 2, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 2, 1, 0, 2, 0, 2, 2, 1, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 2, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 1, 2, 0, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 2, 0, 1, 0, 2, 1, 1, 2, 1, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 2, 1, 0, 1, 2, 2, 1, 1, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 2, 0, 0, 1, 2, 1, 2, 0, 1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 2, 1, 0, 1, 2, 0, 0, 2, 1, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 1, 2, 1, 1, 2, 2, 0, 2, 2, 0, 1, 2, 1, 2, 1, 1, 1, 0, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 1, 1, 0, 0, 2, 0, 1, 2, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 1, 0, 1, 0, 1, 2, 2, 1, 1, 2, 0, 2, 1, 1, 1, 1, 2, 0, 2, 2, 2, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 2, 0, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 0, 2, 1, 1, 2, 1, 2, 1, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 1, 2, 0, 1, 2, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 2, 1, 0, 1, 2, 2, 2, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 2, 1, 1, 2, 0, 0, 2, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 1, 2, 2, 0, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 0, 2, 2, 1, 0, 1, 2, 1, 2, 2, 1, 0, 1, 1, 2, 2, 1, 2, 2, 0, 0, 0, 0, 2, 1, 1, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 2, 1, 2, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 1, 0, 1, 0, 2, 2, 1, 2, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 0, 1, 1, 0, 0, 1, 2, 1, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 0, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2 ] [2]: [111, 9, 65] Linear Code over GF(3) Puncturing of [1] at { 112 } last modified: 2008-09-01
Lb(111,9) = 63 is found by shortening of: Lb(112,10) = 63 is found by truncation of: Lb(121,10) = 72 dB Ub(111,9) = 69 follows by a one-step Griesmer bound from: Ub(41,8) = 23 follows by a one-step Griesmer bound from: Ub(17,7) = 7 is found by considering shortening 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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