Title: New families of perfect linear error-block codes

Authors: Rabiî Dariti; El Mamoun Souidi

Addresses: Mathematics, Informatics and Applications Laboratory, Faculty of Science of Rabat, Mohammed V Agdal University, BP 1014, Rabat, Morocco ' Mathematics, Informatics and Applications Laboratory, Faculty of Science of Rabat, Mohammed V Agdal University, BP 1014, Rabat, Morocco

Abstract: Linear error-block codes are a natural generalisation of linear error correcting codes. In this paper, we revisit all the known results on perfect linear error-block codes. We give the parameters of all perfect codes of minimum π-distance 3 and 4. The existence of new families of perfect codes is proven and their constructions are given. Moreover, some of these families are simultaneously perfect and MDS. Experimental results show that there exists only one class of parameters of perfect linear error-block codes of minimum π-distance 5. It is not likely to find further classes.

Keywords: source coding; linear error block codes; pi-distance; perfect codes; perfect MDS codes; linear error correcting codes.

DOI: 10.1504/IJICOT.2013.059702

International Journal of Information and Coding Theory, 2013 Vol.2 No.2/3, pp.84 - 95

Received: 20 Mar 2012
Accepted: 12 Jul 2012
Published online: 13 Sep 2014 *

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