# 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.

## Abstract

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 |
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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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