New families of perfect linear error-block codes. (1st January 2013)

• Record Type: Journal Article
• Authors: Dariti, Rabiî; Souidi, El Mamoun
• Is Part Of: International journal of information and coding theory. Volume 2:Number 2/3(2013)
• Page Start: 84
• Page End: 95
• Publication Date: 2013-01-01
• Subjects: source coding -- linear error-block codes -- ≺-distance -- perfect codes -- perfect MDS codes; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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 ≺ -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 ≺ -distance 5. It is not likely to find further classes.