On partitions of the  q ‐ary Hamming space into few spheres | Zendy

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On partitions of the q ‐ary Hamming space into few spheres

Author(s) -

Klein Andreas,

Wessler Markus

Publication year - 2006

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20083

Subject(s) - hamming space , mathematics , generalization , hamming distance , hamming bound , hamming code , partition (number theory) , combinatorics , spheres , binary number , space (punctuation) , discrete mathematics , algorithm , arithmetic , block code , mathematical analysis , computer science , physics , decoding methods , astronomy , operating system

In this paper, we present a generalization of a result due to Hollmann, Körner, and Litsyn [9]. They prove that each partition of the n ‐dimensional binary Hamming space into spheres consists of either one or two or at least n + 2 spheres. We prove a q ‐ary version of that gap theorem and consider the problem of the next gaps. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 183–201, 2006

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