lower bound: | 166 |
upper bound: | 166 |
Construction of a linear code [224,5,166] over GF(4): [1]: [226, 5, 168] 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, 1, 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, 0, w, 1, w, 0, w, 0, 1, w^2, 0, 1, w^2, 0, w^2, 0, 1, w, w^2, 0, 1, 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, 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, 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, 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, 0, 1, 1, w, w, w^2, w^2, 0, 1, 1, 1, w, w, w^2, 0, 0, 0, 1, 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, 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, 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, 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, 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, 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, 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, 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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 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, 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, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [224, 5, 166] Linear Code over GF(2^2) Puncturing of [1] at { 225 .. 226 } last modified: 2002-05-01
Lb(224,5) = 166 is found by truncation of: Lb(226,5) = 168 BKW Ub(224,5) = 166 follows by a one-step Griesmer bound from: Ub(57,4) = 41 is found by considering truncation to: 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
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