The weight distributions of some irreducible cyclic codes of length $p^n$ and $2p^n$

Abstract

In this paper, an algorithm is given for computing the weight distributions of all irreducible cycliccodes of dimension $p^jd$ generated by $x^{p^j}-1$, where $p$ is anodd prime, $j\geq 0 $ and $d > 1$. Then the weight distributions ofall irreducible cyclic codes of length $p^n$ and $ 2p^n $ over$F_q$, where $n$ is a positive integer, $p$, $q$ are distinct oddprimes and $q$ is primitive root modulo $ p^n$, are obtained. Theweight distributions of all the irreducible cyclic codes of length$3^{n+1}$ over $F_5$ are also determined explicitly.