lower bound: | 64 |
upper bound: | 69 |
Construction of a linear code [100,9,64] over GF(4): [1]: [100, 9, 64] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 1, w, 0, 0, 0, 0, 0, 0, w, w, w, w^2, 0, w, 0, 1, 1, w, w, w^2, 0, 1, 0, 1, w^2, w^2, 1, w, 1, w^2, w^2, 1, 0, w, 1, w, w^2, w^2, w, w^2, w^2, w^2, w, 1, 1, w^2, 0, 0, 1, w, 1, w^2, 1, w^2, 1, w, w^2, w, 0, w^2, 1, 1, w^2, 0, w^2, w^2, w^2, w, w, w, 0, 1, w, w^2, 0, 0, w, 0, 1, 1, w, w^2, 1, w, w^2, w^2, w^2, w, w, 1, 0, 1, 0, w, 0, 1, w ] [ 0, 1, 0, w, 1, 0, 0, 0, 0, 0, 0, w, w, w, w^2, 0, w, 0, 1, 1, w, 1, 1, w, w, 1, 1, 0, 0, w, 0, w, w^2, w, 0, w, 1, w, w^2, 0, w, 0, w^2, 1, w^2, w^2, w^2, 1, w, w, w, 0, 0, w^2, 1, 1, 0, 1, 1, w^2, 0, w, 1, w, w, 0, w, w^2, 1, w, w^2, w^2, w^2, w, w^2, w, w^2, 1, 1, 0, 1, 0, 0, w^2, w^2, w, w, 1, w, w, 0, w, 0, 1, w, 0, w, 0, 1, w ] [ 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, 1, 0, w^2, 0, w, w, 1, w, 0, 0, 1, 1, 0, 0, 0, 0, w^2, 1, w^2, 1, 1, w, w^2, 0, w^2, w, 1, w, w^2, 0, 0, 1, 0, 1, w^2, w^2, 0, 0, w^2, 0, w^2, w^2, w, 1, 1, w^2, w^2, 1, w, w^2, 0, 0, w^2, 0, w^2, w, 0, w, w^2, w, w^2, 0, 0, 0, 0, 0, w^2, w, w^2, w, w^2, 1, 0, w, w, w^2, w^2, 1, 1, 0, w^2, 0, w^2, 0, w, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, w, 0, w, 0, w^2, w^2, w, 1, w^2, 0, 0, w, w^2, w, w^2, 1, w, w^2, w, 1, w, w, 0, w, 1, w^2, 0, 1, 0, 1, w^2, 0, w, w, 1, w, w^2, w, 1, 0, w^2, w, 1, w^2, w, w^2, 1, 1, w^2, 1, w, 0, 1, 0, w, 1, 0, 1, w^2, 1, 0, w^2, w^2, w^2, 1, 1, 0, 1, 1, w^2, 0, w, 0, 0, w, 0, 0, w, w, w^2, 0, 0, w^2, w, w^2, 0, 1, w, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, w^2, w, w, 0, w^2, 1, 0, w^2, w, w, 0, w^2, 0, 1, w, 0, 1, w^2, w, w^2, 0, 0, w^2, w^2, 0, 0, w, 0, 0, w^2, w, 0, w, 0, w^2, 1, 0, 1, w, 0, 1, w, 0, w^2, w, w^2, w^2, w, 0, w, 1, 1, w, 1, w, w, 1, 1, 1, w, 0, w^2, 1, 0, w^2, w, 0, 1, 1, 1, 1, w^2, 0, 1, 1, 0, 1, 0, w, 0, 0, 1, w^2, 1, 0, w^2, 1, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, w, w^2, 1, w, w, 0, w^2, w^2, 0, w^2, 1, w^2, 1, 0, 0, 0, 1, w, w, w, 1, 0, w, 0, 1, 0, 1, w^2, 0, w, w^2, 0, 0, w, 0, 0, 0, w^2, w, 1, w^2, w^2, w^2, 1, w^2, w, 1, w^2, w^2, 0, w^2, 0, w, 0, 1, w^2, 0, 1, w^2, 0, 1, 0, w, w, w^2, w, w^2, w^2, w, w^2, 0, w^2, w^2, 0, 0, 0, w, w^2, w, 0, w^2, w^2, w, 1, w, w, 0, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, w, w^2, w^2, w^2, 0, 1, w^2, w, w, 0, w^2, 0, w, w, 1, 0, w^2, 1, w, w^2, 1, w, 0, w, w, 1, w^2, w^2, w^2, w^2, 1, w^2, w, 0, 0, 1, w^2, w^2, w, 1, 0, w, w, 1, w, w^2, w, w, w, w, w^2, w^2, w^2, w^2, 1, 0, 1, 1, 0, 1, w, 1, w, 1, w^2, 0, w^2, w^2, 1, 0, w^2, 0, w^2, 0, w^2, 1, 0, 1, 1, w, 0, w^2, 0, 1, w, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, w^2, 1, w^2, w^2, w^2, w, w, 0, 1, 0, w^2, 1, w^2, w, 1, 0, 1, 1, w^2, 0, w^2, 0, 0, 0, 1, 0, 1, 1, w, 0, 1, 1, 1, 0, 0, w^2, 0, 0, w^2, w^2, w, 1, 1, w^2, 0, w, 0, w^2, w, w, 0, 1, 1, 1, w^2, 0, w^2, w^2, 0, w^2, 1, 0, 1, w^2, w, 1, w, 1, 0, 1, w^2, w, 0, 0, w^2, w, w, 0, 1, w, w^2, w^2, 0, w^2, 0, 1, w, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, 1, w^2, w^2, w, 1, w^2, 1, w^2, 0, w, w^2, 1, w^2, w, 0, 1, 0, 0, 1, 0, 1, 0, 0, w, w, 1, w^2, w, w, w^2, w^2, 0, 0, 0, 1, w^2, w, w, w^2, w^2, 0, 0, w^2, 1, w^2, w, 0, 1, 0, w, w^2, w^2, 0, 1, 0, 1, 1, 0, 1, 0, w^2, w^2, w^2, w, w^2, 0, w^2, 0, w^2, w^2, 0, 0, w, 0, w, 1, 1, w, w^2, w, w^2, w, w, w^2, w^2, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2012-03-29
Lb(100,9) = 63 is found by shortening of: Lb(101,10) = 63 is found by truncation of: Lb(102,10) = 64 DaH Ub(100,9) = 69 follows by a one-step Griesmer bound from: Ub(30,8) = 17 follows by a one-step Griesmer bound from: Ub(12,7) = 4 is found by construction B: [consider deleting the (at most) 6 coordinates of a word in the dual]
Notes
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