Further results on the covering radious of small codes

Kéri, Gerzson and Östergard, P. R. J. (2007) Further results on the covering radious of small codes. Discrete Mathematics, 307. pp. 69-77.

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The minimum number of codewords in a code with t ternary and b binary coordinates and covering radius R is denoted by K(t,b,R). In the paper, necessary and sufficient conditions for K(t,b,R)=M are given for M=6 and 7 by proving that there exist exactly three families of optimal codes with six codewords and two families of optimal codes with seven codewords. The cases M<=5 were settled in an earlier study by the same authors. For binary codes, it is proved that K(0,2b+4,b)>=9 for b>=1. For ternary codes, it is shown that K(3t+2,0,2t)=9 for t>=2. New upper bounds obtained include K(3t+4,0,2t)<=36 for t>=2. Thus, we have K(13,0,6)<=36 (instead of 45, the previous best known upper bound).

Item Type: ISI Article
Uncontrolled Keywords: covering code, covering radius, mixed code, surjective code
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:30
Last Modified: 11 Dec 2012 15:30
URI: https://eprints.sztaki.hu/id/eprint/5082

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