lower bound: | 172 |
upper bound: | 172 |
Construction of a linear code [232,5,172] over GF(4): [1]: [236, 5, 176] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, w, 0, w^2, w, w^2, 1, w, 1, 1, 1, w^2, w, 1, 0, w, 0, w^2, w^2, 0, 0, w^2, w, w^2, w, w, w, w, 0, 0, w^2, w^2, 0, w^2, w, 0, w^2, w, w^2, 0, w^2, w, w, w^2, w^2, w^2, 1, 1, w, 1, 1, w^2, 1, 1, 1, 1, w^2, 1, 0, 1, 0, w^2, w^2, w^2, 0, 0, 0, 0, 0, 1, 1, w, w, 0, 1, 1, 0, 0, w, w, w^2, w, 0, w, 0, 0, w, 1, 1, w^2, 1, w^2, w^2, 1, 1, w^2, w^2, w^2, w^2, w^2, w, w^2, 0, 1, 1, w, w, w, w, w, w, w, 0, w^2, w, w^2, w^2, 0, 0, 1, 0, w^2, w^2, w^2, 0, w, 1, 0, w, 0, w, w, 1, 0, w, 1, w^2, 0, 1, 0, w^2, 1, 0, w, 0, 0, 0, w^2, 1, 1, 0, 0, w^2, 0, 1, w^2, w^2, 1, 0, w^2, 1, w, 0, 1, 1, 1, w, w^2, w^2, w, 1, 1, 0, w^2, w^2, w^2, w^2, 0, w^2, w^2, w, w, 0, w, w, 1, 0, w, w, w, w, 0, w, 0, w, w, w, w, w^2, w, 0, w^2, 1, w^2, 1, w^2, w, w^2, w, 1, 0, 1, w^2, w, w^2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, 1, 0 ] [ 0, 1, 0, 0, 0, 1, 1, w, w^2, 1, 1, 0, w, 0, 1, w, w, w^2, 1, w, w^2, w^2, w^2, w, w, w^2, w, w, w^2, 0, w^2, 1, 1, 1, 1, w^2, w^2, w, 1, 1, 0, w^2, 1, w, 1, w^2, w, w, w^2, w, 1, 1, 1, w^2, w^2, w, w, w, 1, w^2, w, w, w, w^2, w^2, w, 0, w^2, w, w, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, w, 1, 1, w, w^2, 0, 1, w, 1, 0, w, 0, 1, w^2, 0, 1, w, w^2, w^2, 0, w, w^2, 0, 1, 1, 1, 0, w^2, 1, 1, 1, 1, 0, 1, w, w^2, w, w^2, w, w^2, w, 1, w, w^2, w^2, w, 1, w, w^2, w^2, w, w, w^2, 0, w^2, w, 0, w, w, 1, w^2, 1, 0, 1, w, w, 1, 0, w, 1, w, 0, w^2, w, w^2, 1, 1, w^2, 0, 0, 1, w, w^2, 0, 1, w, 1, 0, 1, w^2, 0, 1, 1, 1, w, w^2, 0, 1, 1, 1, 1, 0, 1, 1, w, 0, w^2, 1, 1, w^2, w, w, w^2, 0, w, w, w^2, w^2, 1, w^2, 0, w^2, w, w, 1, w, 0, w, 1, w^2, 1, w, w^2, 0, w, 1, 1, w^2, 0, w, 1, w, 0, w, w, w^2, w, w, w^2, w, w, w^2, 0, 0, 1, w ] [ 0, 0, 1, 0, 0, w^2, w, w^2, 1, 0, w, w^2, w, w^2, w^2, w^2, w^2, 0, w, w^2, w^2, 0, 1, w, 0, w, 0, 1, 1, w, 1, 1, 0, 0, 0, 1, 0, 1, 1, w^2, w^2, w, 0, 1, w, w^2, w^2, w^2, w, 0, 0, 1, 0, w^2, w, w^2, 0, 1, w^2, 0, w^2, w, w, 0, 1, 0, 1, w, 0, 1, 0, w, w^2, w^2, 0, w, w^2, 1, w^2, w, 1, w, 1, w, w^2, 1, w^2, 0, w^2, 1, w^2, w, 1, w^2, w, 0, w, 1, 0, 0, 0, w^2, w^2, 1, 0, 1, w, w, w^2, 1, w^2, w, 0, w, 0, w, 1, 0, w, 1, w^2, 0, w, 0, w, 1, w^2, 0, w, w, 0, w, 1, w^2, 0, w, 0, 1, 1, 1, 0, 1, 1, w, 0, w^2, w, w, 0, 0, w, w^2, w^2, 1, 1, 0, 0, 1, w^2, 1, 1, 0, w^2, w, 0, w^2, 1, w, w, w^2, 1, w, w^2, 1, 1, 0, w^2, 1, 1, w, 0, 1, w^2, w^2, w, 0, w, w^2, w^2, w, 0, 1, 1, 1, w, w^2, 1, 0, w, w^2, 1, w^2, 1, 0, 0, w^2, w, w, w^2, 1, 0, 1, w^2, 0, 1, 1, w, w^2, 0, w, w, w^2, w, w^2, w^2, w, 1, 0, w^2, w, w, 0, 1, 0, w, 1 ] [ 0, 0, 0, 1, 0, w^2, w, w, 1, 1, w, w^2, w, w, w, 1, 1, w^2, 0, 0, 0, w^2, w^2, 0, w, 1, w^2, w, w, 1, w^2, w, w^2, w, w, w^2, w, w, w, 1, 1, 1, w, 0, w, w^2, w^2, w, w^2, 0, 0, 0, 1, w^2, w, w, 1, 0, w, 1, w^2, w, w, 1, 0, 1, 0, w, 0, 1, w^2, 0, 0, 0, w, 1, 0, w^2, 1, 0, w^2, 1, w^2, 1, 0, w, 0, w^2, 1, w, 1, 1, w^2, 0, w, 1, w^2, 0, 0, 0, 1, w^2, w, 0, 0, 1, w^2, w^2, w^2, 0, w^2, w, 0, w^2, w^2, 0, w, w, 1, w^2, 1, w^2, 0, w^2, 1, w, 0, w, 1, 0, w, 0, w, 1, w^2, 0, w^2, w^2, w^2, 0, 1, 1, 1, w^2, 0, w, w, w, 0, 0, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, w, w, w, 1, 1, w, 0, w^2, 1, 1, 1, w^2, 0, 1, w^2, w^2, w, 0, w, w, 0, w^2, w^2, 0, 0, w, w, w, w^2, w^2, w^2, 1, 1, 1, 1, w, w^2, 0, 0, w^2, w, 1, w^2, 1, 1, 1, w^2, w, w^2, 1, w, w, w^2, 0, w, w^2, w^2, 0, 1, w^2, 1, 1, 0, 0, 0, 1, 0, w, w^2, 1, 1, 1, w, 0, 1, w^2, 1 ] [ 0, 0, 0, 0, 1, w^2, w^2, 0, 1, 0, 1, 0, w, w^2, 1, 1, 1, w^2, 1, w, 0, w^2, 1, 0, 0, w^2, w^2, w^2, 1, 1, 0, w^2, w^2, w, w, w, w^2, 1, w, w^2, 1, w, 0, 1, 0, w, 0, w^2, w, 1, w, w, w, 0, 0, w, w, w, 1, w^2, 1, 0, 0, 1, w, w^2, 1, 0, 0, 1, w, w^2, w^2, w^2, 1, w, w^2, 0, 0, 0, w, w^2, 1, 0, 1, w, 0, 0, 1, 0, w, w^2, 1, w^2, w, 1, w, w^2, 1, w, w^2, 1, 1, w^2, w^2, w, 0, w^2, 0, 1, w, w^2, w^2, 0, 1, w, 0, 0, w^2, w^2, w^2, w, w^2, 0, 0, w, w, w^2, w, w^2, 1, 1, 1, w^2, w, w^2, 1, 0, 0, 0, w, w^2, 1, 1, w^2, 1, w, 0, w, 1, w^2, w, 1, w, 0, 1, 1, w^2, w, w^2, 1, w, w^2, 0, 1, 0, w, w, 0, 1, 1, w^2, w^2, w^2, 0, 1, 0, 0, 0, w, w^2, w^2, 0, 0, 1, w, w^2, 1, 1, 0, 0, 0, w, 1, w^2, w^2, 0, 0, w, w, 0, w^2, 1, 1, w, w^2, 1, 1, 0, w, w^2, w^2, w, w^2, 1, w, w, 0, 1, w, 1, w^2, w, 1, 0, 1, w^2, w, 0, 0, 0, w^2, w, w^2, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [232, 5, 172] Linear Code over GF(2^2) Puncturing of [1] at { 233 .. 236 } last modified: 2002-04-15
Lb(232,5) = 172 is found by truncation of: Lb(236,5) = 176 BKW Ub(232,5) = 172 follows by a one-step Griesmer bound from: Ub(59,4) = 43 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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