New Results on Codes with Covering Radius 1 and Minimum Distance 2 |
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| Authors: | Patric?R?J??sterg?rd J?rn?Quistorff Email author" target="_blank">Alfred?WassermannEmail author |
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| Institution: | (1) Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015, HUT, Finland;(2) Helsinki University of Technology, Speckenreye 48, 22119 Hamburg, Germany;(3) Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany |
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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)  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).Supported in part by the Academy of Finland under grant 100500. |
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