Prime Decomposition Problem for Several Kinds of Regular Codes

Given a class C of codes. A regular code in C is called prime if it cannot be decomposed as a catenation of at least two non-trivial regular codes in C. The prime decomposition problem for the class C of codes consists in decomposing regular codes in C into prime factors in C. In this paper, a general approach to this problem is proposed, by means of which solutions for the prime decomposition problem are obtained, in a unified way, for several classes of codes. These classes are all subclasses of prefix codes and can be defined by binary relations.