lower bound: | 119 |
upper bound: | 125 |
Construction of a linear code [176,9,119] over GF(4): [1]: [177, 9, 120] Linear Code over GF(2^2) code found by Tatsuya Maruta Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, w^2, 0, w^2, w^2, w, w, 0, 1, w^2, 1, 1, 0, 0, w^2, 1, 0, 1, w^2, 0, 1, w, w, w^2, 1, w, 1, w^2, 0, 1, w, 1, 1, 0, w, 0, 0, 0, 1, 1, 0, w, 1, w^2, 0, w, w^2, 0, 0, w^2, 0, w, w^2, w^2, w^2, w, w, 1, w, w, w, w^2, 0, w^2, w^2, 0, 0, w, w, 1, 1, w^2, w, w, w, 0, w, w^2, w^2, w, 0, w, 1, 1, w, 0, w, w, w, 1, w^2, w^2, w, w, 0, 0, 1, 1, 0, 1, w, w, w, w^2, w, w, 1, 1, 1, w, 0, 1, 0, 0, 1, w, 0, 1, w^2, w, 0, w^2, w^2, 0, 0, 0, w, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, w^2, 1, w, w, w^2, 0, 1, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 1, w^2, 0, w, w, 1, 1, 0, 1, 0, w, w^2, 1, w, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, w^2, 0, w^2, w^2, w, w, 0, 1, w^2, 1, 1, 0, 0, w^2, 1, 0, 1, w^2, 0, 1, w, w, w^2, 1, w, 1, w^2, 0, 1, w, 1, 1, 0, w, 0, 0, 0, 1, 1, 0, w, 1, w^2, 0, w, w^2, 0, 0, w^2, 0, w, w^2, w^2, w^2, w, w, 1, w, w, w, w^2, 0, w^2, w^2, 0, 0, w, w, 1, 1, w^2, w, w, w, 0, w, w^2, w^2, w, 0, w, 1, 1, w, 0, w, w, w, 1, w^2, w^2, w, w, 0, 0, 1, 1, 0, 1, w, w, w, w^2, w, w, 1, 1, 1, w, 0, 1, 0, 0, 1, w, 0, 1, w^2, w, 0, w^2, w^2, 0, 0, 0, w, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, w^2, 1, w, w, w^2, 0, 1, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 1, w^2, 0, w, w, 1, 1, 0, 1, w^2, w, w^2, 1, w, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, w^2, 1, 1, w, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, w^2, 1, 1, w, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w, 0, w, 0, w^2, w^2, w^2, 0, w, w^2, 1, 0, w^2, w, 0, w, 0, w, w, 0, w, w^2, w^2, w, w, 1, w, 0, 1, w, 1, w^2, 1, 0, w, w^2, 1, 0, 0, w^2, 1, w^2, 1, 0, w^2, w^2, w, w, w, w, 1, w^2, 0, w^2, 1, 1, w, w^2, w^2, 0, w^2, 1, w^2, w^2, w^2, 1, 1, w, 1, 1, 0, 0, w, w^2, 1, w, w, 1, 1, 0, 0, 0, 0, w, w, 1, 1, w, w^2, 1, 0, 0, w, w, 1, w, w, w^2, w^2, w^2, w, w^2, 0, w^2, w^2, 1, w, w, w^2, 0, w^2, w, 1, 1, 1, 1, w^2, w^2, 0, w, w^2, w, w^2, 0, 0, w, w^2, 1, 0, w, w^2, w, 1, w, 0, 1, w, 1, 1, w^2, w^2, 1, 0, 1, 1, 0, 1, 0, 1, w^2, 0, w, w^2, 1, 0, w^2, w^2, w^2, 0, 1, 0, 1, w, w^2, w, w^2, 1, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, 0, 0, w, 0, 1, 0, 0, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, 0, 0, w, w, 1, 0, 0, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 0, w, w, 1, 1, 0, w^2, w, w^2, w^2, 0, 0, w, w^2, 0, w^2, w, 0, w^2, 1, 1, w, w^2, 1, w^2, w, 0, w^2, 1, w^2, w^2, 0, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, w, 0, 1, w, 0, 0, w, 0, 1, w, w, w, 1, 1, w^2, 1, 1, 1, w, 0, w, w, 0, 0, 1, 1, w^2, w^2, w, 1, 1, 1, 0, 1, w, w, 1, 0, 1, w^2, w^2, 1, 0, 1, 1, 1, w^2, w, w, 1, 1, 0, 0, w^2, w^2, 0, w^2, 1, 1, 1, w, 1, 1, w^2, w^2, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w, 1, 0, w, w, 0, 0, 0, 1, 0, w, w, 1, w, 0, w^2, w, 1, w, w^2, 1, 1, w, 0, w^2, w, 0, w, w^2, 0, 0, w, w, w^2, w, 0, 1, 1, w^2, w^2, 0, w^2, 0, 1, 0, w^2, 1, 0, w, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 0, w, w, 1, 1, 0, w^2, w, w^2, w^2, 0, 0, w, w^2, 0, w^2, w, 0, w^2, 1, 1, w, w^2, 1, w^2, w, 0, w^2, 1, w^2, w^2, 0, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, w, 0, 1, w, 0, 0, w, 0, 1, w, w, w, 1, 1, w^2, 1, 1, 1, w, 0, w, w, 0, 0, 1, 1, w^2, w^2, w, 1, 1, 1, 0, 1, w, w, 1, 0, 1, w^2, w^2, 1, 0, 1, 1, 1, w^2, w, w, 1, 1, 0, 0, w^2, w^2, 0, w^2, 1, 1, 1, w, 1, 1, w^2, w^2, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w, 1, 0, w, w, 0, 0, 0, 1, 0, w, w, 1, w, 0, w^2, w, 1, w, w^2, 1, 1, w, 0, w^2, w, 0, w, w^2, 0, 0, w, w, w^2, w, 0, 1, 1, w^2, w^2, 0, w^2, 0, 1, w, w^2, 1, 0, w, w ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [176, 9, 119] Linear Code over GF(2^2) Puncturing of [1] at { 177 } last modified: 2006-10-04
Lb(176,9) = 119 is found by truncation of: Lb(177,9) = 120 MST Ub(176,9) = 125 is found by considering shortening to: Ub(175,8) = 125 Da1
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
|