lower bound: | 37 |
upper bound: | 37 |
Construction of a linear code [52,4,37] over GF(4): [1]: [55, 4, 40] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 1, w, w^2, w^2, w^2, 1, w^2, w, w^2, w^2, 0, 0, w, w, w, w^2, w^2, 1, 1, 0, w^2, w, 1, w^2, w, w, w, w^2, 0, w^2, w^2, w^2, w, 1, w, w, 1, w, 0, w^2, 1, w, 0, 1, 0, 1, 1, 1, 1 ] [ 0, 1, 0, 0, 1, w^2, w, 0, w^2, 0, w, w, w^2, w, w^2, 1, 0, w, 1, 0, 0, 0, 1, w, w^2, w, w, w^2, w^2, w, 0, w^2, 1, 0, 0, 1, 1, 0, 1, 1, 0, w, 1, w, 1, w^2, w^2, w^2, w, w, 1, 0, 1, w^2, 1 ] [ 0, 0, 1, 0, w^2, w, 1, w, 1, 1, w^2, w^2, 0, 0, 0, w^2, w, w^2, 1, w, 0, w, 1, 0, w^2, w^2, 0, w, 1, w, w^2, w^2, 0, 0, w^2, w, 0, w^2, w^2, 0, 1, w, w, w^2, 1, w^2, 0, w^2, 0, w, 1, 1, w, 1, w^2 ] [ 0, 0, 0, 1, w^2, 1, w^2, 0, 0, w, w^2, 0, 1, 1, 0, 0, w^2, 1, w^2, 1, w^2, 0, w, w, 0, 0, 0, w, w, w^2, 0, w, w, w, w, 1, w^2, 1, 1, 1, w, w^2, w, w, 0, w, w^2, w^2, w, 0, 1, 1, w^2, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [52, 4, 37] Linear Code over GF(2^2) Puncturing of [1] at { 53 .. 55 } last modified: 2001-12-17
Lb(52,4) = 37 is found by shortening of: Lb(53,5) = 37 is found by truncation of: Lb(56,5) = 40 BKW Ub(52,4) = 37 is found by considering truncation to: Ub(51,4) = 36 LMH
LMH: I. Landgev, T. Maruta, R. Hill, On the nonexistence of quaternary [51,4,37] codes, Finite Fields Appl. 2 (1996) 96-110.
Notes
|