lower bound: | 10 |
upper bound: | 11 |
Construction of a linear code [27,11,10] over GF(3): [1]: [36, 18, 12] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 0, 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, 0 ] [2]: [34, 18, 10] Linear Code over GF(3) Puncturing of [1] at { 35 .. 36 } [3]: [27, 11, 10] Linear Code over GF(3) Shortening of [2] at { 28 .. 34 } last modified: 2008-05-17
Lb(27,11) = 10 is found by shortening of: Lb(34,18) = 10 is found by truncation of: Lb(36,18) = 12 Ple Ub(27,11) = 11 is found by considering shortening to: Ub(24,8) = 11 BS
Ple: V. Pless, On a new family of symmetry codes and related new 5-designs, Bull. Amer. Math. Soc. 75 (1969) 1339-1342.
Notes
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