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

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