New Results on Codes with Covering Radius 1 and Minimum Distance 2

Authors:
Patric R. Östergård;Jörn Quistorff;Alfred Wassermann
Affiliations:
Department of Electrical and Communications Engineering, Helsinki University of Technology, Finland 02015;Helsinki University of Technology, Hamburg, Germany 22119;Department of Mathematics, University of Bayreuth, Bayreuth, Germany 95440
Venue:
Designs, Codes and Cryptography
Year:
2005

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Abstract

The minimal cardinality of a q-ary code of length n and covering radius at most R is denoted by Kq(n, R); if we have the additional requirement that the minimum distance be at least d, it is denoted by Kq(n, R, d). Obviously, Kq(n, R, d) 驴 Kq(n, R). In this paper, we study instances for which Kq(n,1,2) Kq(n, 1) and, in particular, determine K4(4,1,2)=28 24=K4(4,1).