Idempotents Generators for Minimal Cyclic Codes of Length pnq.

Let p and q be distinct positive prime numbers and l positive integer such that gcd(l, pq) = 1. For a natural number n >= 1, let C-pnq be a cyclic group of order p(n)q and F-l finite field with l elements. In this paper we explicitly present the primitive idempotents of the group algebra FlCpnq under some further restrictions on l, p and q. These idempotents generate the minimal ideals of FlCpnq, hence the minimal cyclic codes of length p(n)q. Our computation is based on techniques developed by Bakshi and Raka (Finite Fields Appl 9(4): 432-448, 2003) and Ferraz and Polcino Milies (Finite Fields Appl 13: 382-393, 2007). A particular example for codes of length 245 is computed and we believe that this points out some mistakes in current literature on this subject.