The weight distribution for any irreducible cyclic code of length \(p^m\)
Irreducible cyclic codes are a speical class of cyclic codes. They are minimal cyclic codes and it is of theoretical significance to study them. In this paper, irreducible cyclic codes with prime power length are investigated. The weight distributions of such codes are presented, which generalize the results of \textit{A. Sharma} and \textit{G. K. Bakshi} [Finite Fields Appl. 18, No. 1, 144--159 (2012; Zbl 1231.94074)]. Furthermore, some irreducible cyclic codes with one-weight and two-weight are constructed. It is shown that the family of one-weight and two-weight irreducible cyclic codes is an important component that describes the family of irreducible cyclic code of prime power length.
scientific article; zbMATH DE number 6916495