lower bound: | 148 |
upper bound: | 152 |
Construction of a linear code [208,7,148] over GF(4): [1]: [208, 7, 148] Linear Code over GF(2^2) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, 0, w^2, 0, w, w, 1, 1, w, w, w, w, 1, w^2, w^2, w^2, w^2, w, w, 1, 0, 1, w, 1, w, w^2, w^2, w, 0, 0, 1, 0, 1, 0, 1, w, w, w^2, w^2, w^2, 1, w^2, w^2, 1, 1, w, w^2, 1, w^2, w^2, w, 1, w^2, w^2, w, w, w, 1, w^2, w, w, w, w, 1, w^2, 0, 0, 0, 0, 0, 0, w^2, 0, w^2, w, 0, w, 0, w, 0, 0, w^2, 0, w^2, 0, w^2, 0, w^2, w, w, w, 1, w, 0, 1, 1, w, w, w, 1, 1, 1, w^2, 1, w, w, w^2, w, 1, 1, w, w^2, w^2, w, w, 1, 1, 1, 1, w^2, w^2, 1, 1, w^2, w, 0, 1, 0, w^2, 0, 1, 1, 1, w, w, w, w, 0, 0, 1, 0, w^2, w^2, 1, 0, 0, w^2, 0, 0, 0, 0, 0, 0, 0, 1, w, w^2, 0, w^2, 1, w, 1, 1, w^2, w^2, w, w, w^2, w, w^2, w, 1, w, w, 0, w^2, 1, w, 1, w^2, w^2, w^2, 0, 0, 0, 0, w^2, w, w^2, 1, 1, 1, w, 1, 1, w, 0, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, w^2, w^2, w, 0, 0, 0, 0, 1, 0, w^2, w, 0, 0, w^2, w, w, 1, w^2, w, 1, 0, 1, w, 0, w, 0, w, 0, w^2, 1, w, 1, w, w, 1, w, w, 0, w^2, w^2, w, 0, w, 1, w^2, 0, w^2, w^2, w^2, w, w, 0, 1, 0, 0, w^2, w, 0, w, w^2, w^2, 1, 0, w, w^2, w, 1, 1, 1, w, w, 1, 1, 0, 0, 1, w, w, 1, 0, 0, w^2, 1, 1, w, w^2, 0, w, 1, w^2, 0, 1, w^2, w^2, 1, 0, w, 0, 1, 1, 1, w, 1, w^2, 0, 1, 0, w^2, 0, w^2, 1, w^2, 0, w^2, w, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, w^2, 0, w^2, 1, w, w, 0, w^2, w, w^2, 1, w, 1, 1, 1, 0, 0, 1, w^2, w^2, w, 1, 0, 1, w^2, 0, 1, 1, w, 0, w, w, w^2, w^2, w^2, 0, 0, w, 0, 1, 0, 0, 1, w, 0, 1, w, w, 0, w^2, 1, w^2, w, w, w, w^2, 1, 0, w^2, w, 0, w, w, w^2, 0, 0, w, w^2, w, w^2, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, w^2, w, w^2, 0, 0, w^2, 0, 1, w, w, w, 1, 1, 0, 0, 1, w^2, w^2, 1, w^2, w, w, 0, w^2, w^2, 1, w, 1, w^2, w^2, 1, w^2, w^2, 0, w^2, 1, 1, w^2, 1, 1, 0, w, 0, 0, w^2, w^2, w, 0, 0, w^2, w^2, 0, 1, 1, 1, w, w^2, 0, w^2, w, 1, 0, w^2, 1, 1, w, 1, w, w^2, w^2, w^2, 1, 1, w^2, 1, 0, 0, 1, w, w, 0, 0, w, w^2, w^2, 1, w^2, 0, 1, 0, 0, 0, 1, 1, 1, 1, w, w^2, w, 0, 0, 1, w^2, w^2, w, w, 1, w, w^2, 1, 0, 1, w, w, w^2, 1, 1, 1, 0, 0, w^2, 0, w^2, w, 1, w^2, 1, w^2, w^2, w, 0, 0, w, 1, 0, 0, w, 1, 1, 0, 0, w^2, w, w^2, 0, w^2, 0, 1, w, w^2, 1, 0, w, w^2, 1, w, w^2, w^2, w, w, w^2, w^2, w, w, w, 1, w, 0, 1, w, 1, w, 1, w, w^2, 1, w, w^2, w, w^2, 0, w, w, w, w^2, 0, 0, 0, w, w, w, 1, w, w, 1, 0, 0, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w^2, w^2, 0, w^2, 1, 0, 0, 1, 1, w^2, 0, w^2, w^2, 1, 0, 1, w, w^2, 0, w, 1, 0, w^2, w^2, w^2, w, 0, 0, 1, w, 0, 1, 1, w^2, w^2, 1, w^2, w^2, w, w^2, w, w^2, w^2, w, w, w^2, w^2, 0, 0, 0, w, 0, w, 0, w^2, 0, 0, w^2, w^2, w^2, 0, w, w, 1, w^2, 1, w, 0, w^2, w, 0, 0, 1, w^2, w^2, w, w^2, 0, w, 1, w, w^2, w^2, 0, w, 1, 1, 0, w, 1, w, 1, 1, w^2, 1, 0, w^2, 1, 0, w, w, 1, 0, w^2, 1, 1, w, w^2, w^2, 0, w, 0, w^2, w, 0, 1, w^2, 1, w^2, 0, w^2, 1, w, w^2, 0, 0, 1, w, w^2, 1, w^2, 1, w, 1, w, 0, 1, w^2, 0, 1, 0, 1, w, w^2, 1, 1, w, 0, 1, 0, 1, 1, w^2, 1, w^2, 0, 0, w, 0, w^2, 1, 0, w, w^2, 0, 1, w^2, 0, 1, w^2, 0, 0, 1, 0, w^2, 1, w, w^2, 0, w^2, w^2, 0, w^2, w, w^2, 0, w, w^2, w, w, 1, 0, w^2, w, 0, 1, w, 0, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, w^2, 0, 0, 0, 1, w^2, w^2, w, 0, 0, w^2, w^2, 1, w^2, w^2, w, w, w, w^2, 0, w, 0, 1, 1, w, w^2, w^2, w^2, 0, w^2, w, w^2, 1, w, 0, 1, 0, w, w, 0, 1, w, 1, 1, w, w, w^2, w^2, 0, 0, 0, 1, 0, 1, w^2, w^2, 1, 0, 1, 1, 1, w^2, 0, w^2, 0, 1, w, 1, w^2, w, 1, 0, w^2, 1, w, w^2, 1, w^2, 0, w, 0, 0, w^2, w, 0, 1, 1, w, 0, w, w, 1, 0, 1, w^2, w, w, w, 1, w, 0, w^2, 0, 0, 0, w, 1, 1, w^2, w^2, w^2, 1, 0, w, 0, w^2, w, 0, w^2, w^2, 0, w^2, w^2, 1, 1, 1, w^2, 1, 0, w, w, w, 1, 1, w, w^2, 1, w^2, w^2, 0, 0, 1, 1, w, 1, 0, 0, w^2, 0, w, w^2, w, w, 1, 1, 0, 1, 0, w, w, w, 1, 0, 0, w^2, w^2, 0, 0, 0, 1, 1, w, 0, w^2, w, w, w, 1, 1, 0, w^2, w^2, 1, w, 0, w^2, 0, 1, w^2, w, 0, 1, 0, w^2, 1, w^2, w, w^2, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, w^2, 1, 0, 1, 1, 1, w^2, w, 0, w, 0, 1, w, 1, 0, w^2, 0, w^2, w^2, w, 0, w, 1, w^2, w, w^2, w^2, w, w, w^2, 1, w^2, 0, 0, 0, 0, 0, 1, w^2, 1, w, 1, w, 0, w, 0, w^2, w, w^2, w^2, 1, 1, 1, 0, 0, w^2, w^2, w^2, 1, 1, w, w^2, 0, 0, 1, 1, w, 0, w, 1, 1, w, 1, w, 0, 0, w, w^2, w^2, 0, 1, 1, w, w^2, w^2, w^2, 1, w, 0, 1, 0, 1, w, 0, w, w, w, 0, w, 1, 1, w^2, w, 0, 0, w^2, 1, w^2, 0, w^2, 1, 0, 1, 0, 0, w^2, 1, w^2, w, w^2, 1, 0, w, w^2, w, 0, 1, w, w^2, w, 1, w^2, w, w, w, 1, 0, 0, w, 0, w^2, w^2, 1, 0, 0, w, w, w^2, 1, 1, 0, 0, 1, w, w^2, w, 1, w, 1, w, w, 1, w, 1, w^2, 1, w^2, w^2, 1, 1, 1, 1, w, 1, w^2, 0, 0, w^2, 0, w^2, w^2, w^2, w, w^2, w, 1, 0, 1, 0, w, w^2, w, 1, 0, w^2, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, w^2, 0, w, 0, 0, w^2, w^2, w^2, w^2, w, w^2, 1, 1, w^2, 0, w, w^2, 0, w, w, 0, w^2, 1, w, w, 1, 0, 1, w, 0, 1, 1, 1, 0, 1, 0, 1, w, w, 1, w, w, w, 1, 1, w^2, 0, w, w, w^2, w, w^2, 1, 0, w, w^2, 0, w, w^2, w^2, 1, w^2, w^2, 1, 1, 0, w, 0, 1, w, w^2, 0, w^2, w, w, 0, 0, w, w^2, 0, w, 1, w, w^2, w, w^2, w^2, 0, 0, 1, w^2, 1, 1, 1, 0, w^2, 1, 0, w^2, w, w, w^2, 0, w, w^2, w^2, 0, w^2, w^2, 1, w, w^2, 1, w, 0, w, w^2, w, w^2, 1, w^2, 1, w^2, 0, w, w^2, 0, 1, 1, 0, 1, 0, 1, w^2, 1, 0, w, w^2, w, 1, w^2, 0, w, 1, 0, 0, 1, 0, w^2, 0, w^2, w, w^2, 0, 1, w^2, w^2, w, w, 1, w^2, w^2, w, 1, 0, w^2, w, 0, w, w^2, 1, w, 0, w^2, 1, w^2, 1, 1, 0, w, w, 1, w^2, 0, w^2, 1, w^2, 1, w, w, 0, w^2, w, 0, 1, w, 0, w^2, 0, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2009-05-04
Lb(208,7) = 146 is found by truncation of: Lb(210,7) = 148 MTS Ub(208,7) = 152 follows by a one-step Griesmer bound from: Ub(55,6) = 38 follows by a one-step Griesmer bound from: Ub(16,5) = 9 follows by a one-step Griesmer bound from: Ub(6,4) = 2 is found by construction B: [consider deleting the (at most) 4 coordinates of a word in the dual]
Notes
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