lower bound: | 163 |
upper bound: | 163 |
Construction of a linear code [220,5,163] over GF(4): [1]: [221, 5, 164] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, w^2, 0, w, 0, 1, w^2, 0, w^2, w, 0, 1, w, 0, 1, w, w^2, 0, w, w^2, w, 0, 1, w, w^2, w, w^2, 0, 1, w, w^2, 0, 1, 0, w, w^2, w, w^2, 0, 1, w, w^2, 0, w, 1, w^2, 0, 1, w, w^2, 0, 1, 0, 1, w^2, 0, w, w^2, w, w^2, 1, w, w^2, 0, 1, 1, w^2, w, 1, w, w^2, w, 1, w, 0, w, 0, 1, w^2, 0, 1, w^2, 0, w^2, 0, 1, w, w^2, 0, 1, w, w^2, 0, w, w^2, 0, w, w^2, w, w^2, 0, 1, w, 0, 1, w, 0, 1, w, w^2, 0, 1, w^2, w, w^2, 1, w, w^2, 1, w, 0, w^2, 0, 1, w^2, 1, w, w^2, 0, 1, w, w^2, 0, 1, w, w^2, w, w^2, 1, w, 0, 1, w, 0, 0, 1, w^2, 1, w, w^2, 1, w, w^2, 0, 1, w^2, 0, w, w^2, w^2, 0, w, 1, w, 0, 1, w^2, 1, w, w^2, 0, 0, 1, w^2, 1, w, w^2, 0, 1, w, w^2, 1, w, w^2, 0, 1, w, 0, 1, w, 0, 1, w^2, 0, 1, w, 0, w, w^2, 0, w, w^2, w, w^2, 1, 0, w^2, 1, 0, w, w^2, 1, 0, 0, 0, 0, 0, 1, 1, w^2 ] [ 0, 1, 1, 0, 0, 1, 1, 1, w, w, w^2, 0, 0, 0, 1, 1, 1, 1, w, w, w, w^2, 0, 0, 0, 0, 1, 1, w, w, w, w, w^2, w^2, 0, 0, 0, 1, 1, w, w, w, w, w^2, w^2, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, w^2, w^2, w^2, 0, 0, 1, 1, w, w^2, w^2, w^2, 0, 1, 1, w, w, w^2, w^2, 0, 1, 1, 1, w, w, w^2, 0, 0, 0, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, w, w, w^2, w^2, w^2, 0, 0, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, 1, w, w, w^2, w^2, 0, 0, 0, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w, w^2, 0, 0, 1, 1, w, w, w, w^2, w^2, w^2, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w, w^2, w^2, 0, 1, 1, w, w^2, w^2, 0, 0, w, w, 0, 1, w, 1, 1, w ] [ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 0, 1, w^2, 1, w, w, w^2, 0, w ] [ 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, 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, 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, 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, w^2, w^2, w^2, 1, 1, 1, 1, w, w, w, w, w^2, w^2 ] [ 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, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [220, 5, 163] Linear Code over GF(2^2) Puncturing of [1] at { 221 } last modified: 2002-05-01
Lb(220,5) = 163 is found by truncation of: Lb(221,5) = 164 BGV Ub(220,5) = 163 follows by a one-step Griesmer bound from: Ub(56,4) = 40 HLa
HLa: R. Hill & I. Landgev, On the nonexistence of some quaternary codes, Proc. IMA conf. Finite Fields and their Applications, June 1994.
Notes
|