lower bound: | 178 |
upper bound: | 178 |
Construction of a linear code [240,5,178] over GF(4): [1]: [242, 5, 180] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 1, 1, w^2, w^2, 0, 0, 0, 1, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 1, 1, 1, w, w, w^2, w^2, w^2, 0, 1, 1, 1, w, w, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, w, w, w, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 1, 1, w, w, w^2, 0, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 1, 1, w^2, w^2, w^2, 1, 1, 1, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w^2, w^2, 0, 0, 0, 1, 1, w, w, w, 0, 0, 0, 0, w, w, w, w^2, w^2, w^2, w^2, w, 0, w, 0, w^2, 1 ] [ 0, 1, 0, w, w^2, 1, 0, w^2, w, 0, w, 1, 0, w, w^2, 1, 0, w, w^2, 1, 0, w, w^2, 1, w^2, 1, 0, w, w^2, 1, w, w^2, 1, 0, w, w^2, 1, 0, 1, w, 0, w^2, w, 0, 1, w^2, w, 1, w^2, 0, 1, w^2, w, 0, w^2, w, 1, w, 1, w^2, 0, w, 0, w^2, w, 1, 1, w^2, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, w, w^2, 1, 0, w, 1, 0, w, w^2, 1, w, w^2, 1, 0, w, 0, w, w^2, 1, 0, w, w^2, 1, w^2, 1, 0, w, w^2, 1, 0, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, w, 1, w, 0, w^2, 1, w, w^2, 1, 1, 0, w, w^2, w, w, w^2, 1, 0, w, 1, 0, w, w^2, 0, w^2, 1, 1, w^2, w, 0, 1, w, 1, w^2, w, 0, w^2, w^2, w, 1, w^2, 1, w, 0, 1, 0, w, w^2, 1, 0, w^2, 0, w, w^2, 1, w, w^2, 1, w, w^2, 0, w, 1, w, 1, w^2, w, 1, w^2, w, 0, 1, w^2, w^2, w, 0, 1, w, 0, 1, w^2, 1, 0, w, w^2, w, w^2, 1, 0, 0, w, w^2, 1, w, w^2, 1, 0, w, w^2, 1, w^2, w, w^2, w, w, w^2 ] [ 0, 0, 1, w^2, w, 0, 1, w, w^2, 0, w, 1, 0, w, w^2, 1, 0, w, w^2, 1, 0, w, w^2, 1, w, 0, 1, w^2, w, 0, w^2, w, 0, 1, w^2, w, 0, 1, w^2, 0, w, 1, 0, w, w^2, 1, 0, w^2, 1, w, w, 0, 1, w^2, 0, 1, w, 1, w, 0, 0, w, 0, w^2, w, 1, 1, w^2, 0, w, w^2, 1, 0, w, w^2, 1, 0, w, w^2, 1, 0, w, w^2, 1, w^2, w, 0, w^2, w, 0, 1, w^2, 0, 1, w^2, w, 0, w^2, 1, 0, w, w^2, 1, 0, w, 0, w, w^2, 1, 0, w, 0, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, 0, w, w^2, 1, 0, w, w^2, 1, 0, w, w^2, 0, w^2, 1, 1, w^2, 0, 1, w^2, w^2, w, 0, 1, 0, 1, 0, w, w^2, 1, w, w^2, 1, 0, w^2, 0, w, 1, w^2, w, 0, 1, w, 1, w^2, w, 0, w^2, w, w^2, 0, w, 0, w^2, 1, w^2, w, 0, 1, w^2, w, 1, w, 0, 1, w^2, 0, 0, w, 1, 0, w^2, 1, w, w, 1, w^2, w, 1, w^2, w, 0, 1, w^2, w, w^2, 1, 0, w^2, 1, 0, w, w^2, w, 0, 1, 0, 1, w^2, w, w^2, 1, 0, w, 1, 0, w, w^2, 1, 0, w, w^2, w^2, 1, 1, w, w ] [ 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 1, 1, 0, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [240, 5, 178] Linear Code over GF(2^2) Puncturing of [1] at { 241 .. 242 } last modified: 2001-12-17
Lb(240,5) = 178 is found by truncation of: Lb(242,5) = 180 Bo1 Ub(240,5) = 178 is found by considering truncation to: Ub(239,5) = 177 LaM
LaM:
Notes
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