New families of perfect linear error-block codes

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.