lower bound: | 40 |
upper bound: | 40 |
Construction of a linear code [56,4,40] over GF(4): [1]: [57, 5, 40] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 1, w, w^2, 0, w^2, 0, w, 0, w^2, w^2, 1, w, w, 1, 0, 1, 0, w^2, w, 0, w, 1, w^2, 1, w, 1, 1, w^2, 1, 0, 1, 0, w^2, 0, 0, 1, w, w, 1, 1, w, w^2, 1, 0, 1, 0, w, 0, w, 0, 0, w^2, w, w ] [ 0, 1, 0, 0, 1, 1, 0, 1, w, w, w^2, w^2, w, w^2, w^2, 0, 1, 0, 1, w, w^2, 1, w^2, 1, w^2, 0, 1, w^2, 1, w, w^2, 1, 0, 0, w, w^2, 0, w^2, w^2, 0, 1, w^2, w^2, 0, 0, 1, w^2, 0, 1, w^2, 0, 0, w, 1, 1, 0, 1 ] [ 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, w, w, w, w^2, w^2, 0, 0, 0, 0, 1, 1, w, w, w^2, w^2, w^2, 0, 0, 0, 1, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, w, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 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, 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, 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 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [56, 4, 40] Linear Code over GF(2^2) Shortening of [1] at { 57 } last modified: 2001-12-17
Lb(56,4) = 40 is found by taking a subcode of: Lb(56,5) = 40 BKW 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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