lower bound: | 119 |
upper bound: | 121 |
Construction of a linear code [186,7,119] over GF(3): [1]: [188, 7, 121] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 2, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 0, 0, 2, 1, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0, 2, 1, 2, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 2, 1, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2, 2, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 1, 2, 2, 2, 2, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 2, 1, 1, 2, 1, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 2, 1, 1 ] [2]: [186, 7, 119] Linear Code over GF(3) Puncturing of [1] at { 187 .. 188 } last modified: 2008-12-29
Lb(186,7) = 118 is found by truncation of: Lb(188,7) = 120 Koh Ub(186,7) = 121 follows by a one-step Griesmer bound from: Ub(64,6) = 40 follows by a one-step Griesmer bound from: Ub(23,5) = 13 is found by considering shortening to: Ub(22,4) = 13 is found by considering truncation to: Ub(21,4) = 12 HN
Koh: Axel Kohnert, email, 2006.
Notes
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