lower bound: | 39 |
upper bound: | 42 |
Construction of a linear code [72,10,39] over GF(3): [1]: [72, 10, 39] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0, 1, 2, 1, 2, 0, 0, 1, 2, 0, 2, 0, 1, 1, 2, 2, 2, 2, 2, 0, 1, 2, 2, 1, 0, 1, 1, 2, 2, 0, 2, 1, 2, 1, 1, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 2, 2, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 0, 0, 0, 2, 1, 1, 2, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 1, 2, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 1, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 1, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 0, 0, 1, 2, 2, 1, 2, 1, 2, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 2, 2, 2, 0, 1, 1, 2, 1, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 1, 2, 1, 2, 2, 0, 1, 0, 2, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 1, 1, 1, 2, 0, 2, 2, 2, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 0, 2, 1, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 0, 2, 0, 0, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 2, 2, 2, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 2, 1, 2, 2, 1, 2, 1, 0, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 0, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 1, 2, 0, 1, 0, 2 ] last modified: 2003-10-14
Lb(72,10) = 38 is found by shortening of: Lb(78,16) = 38 is found by truncation of: Lb(82,16) = 42 NBC Ub(72,10) = 42 follows by a one-step Griesmer bound from: Ub(29,9) = 14 is found by considering truncation to: Ub(27,9) = 12 is found by construction B: [consider deleting the (at most) 6 coordinates of a word in the dual]
Notes
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