New Linear Codes with Covering Radius 2 and Odd Basis |
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| Authors: | Alexander A Davydov Patric R J Osterga |
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| Institution: | (1) Institute for Problems of Information Transmission, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, GSP-4, Moscow, 101447, Russia;(2) Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015 HUT, Finland |
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| Abstract: | On the way of generalizing recent results by Cock and the second author, it is shown that when the basis q is odd, BCH codes can be lengthened to obtain new codes with covering radius R=2. These constructions (together with a lengthening construction by the first author) give new infinite families of linear covering codes with codimension r=2k+1 (the case q=3, r=4k+1 was considered earlier). New code families with r=4k are also obtained. An updated table of upper bounds on the length function for linear codes with  24, R=2, and q=3,5 is given. |
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| Keywords: | BCH code covering code covering radius finite field length function |
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