×

On the improvements of Althöfer-Sillke inequality. (English) Zbl 0902.05071

Summary: We present a new lower bound and a new upper bound for the average Hamming distance in subsets of binary vector space, which are tight for subspaces of binary vector space. These bounds slightly improve the Althöfer-Sillke inequality in [I. Althöfer and T. Sillke, J. Comb. Theory, Ser. B 56, No. 2, 296-301 (1992; Zbl 0723.05055)], and present a partial solution to the open problem stated by R. Ahlswede and G. O. H. Katona in [Discrete Math. 17, 1-22 (1977; Zbl 0368.05001)].

MSC:

05D05 Extremal set theory
94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory
PDFBibTeX XMLCite