Examples of single‐error‐correcting perfect BCD‐AN codes
Munehiro Goto · Electronics and Communications in Japan (Part I Communications) · 1987
Abstract Perfect AN codes are those with the least redundancy under constant code length and error correcting capability. The existence of perfect codes has been studied for generalized r‐ary represented AN codes and symmetric multivalue represented AN codes to apply them to multivalued arithmetic circuits. In this paper we define single‐error‐correcting perfect BCN (Binary Coded Decimal)‐AN codes and obtain the conditions under which the perfect BCN‐AN codes exist. These conditions do not depend on the weight sequence itself used in BDC representation of code words, but on the class to which the weight sequence belongs. By using these conditions we prove that for some classes of the BCD representation including (8421) representation there exists no perfect BCD‐AN code. For some of the remaining classes we obtain examples of generators of perfect BCD‐AN codes through exhaustive computation.