Fu, Fangwei On the improvements of Althöfer-Sillke inequality. (English) Zbl 0902.05071 J. Math. Res. Expo. 16, No. 3, 325-328 (1996). 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)]. Cited in 3 Documents MSC: 05D05 Extremal set theory 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory Keywords:Hamming distance; binary vector space; Althöfer-Sillke inequality Citations:Zbl 0723.05055; Zbl 0762.05040; Zbl 0368.05001 PDFBibTeX XMLCite \textit{F. Fu}, J. Math. Res. Expo. 16, No. 3, 325--328 (1996; Zbl 0902.05071)