Weight enumerators of all irreducible cyclic codes of length n

Abstract

Let [Formula: see text], where [Formula: see text] are distinct odd primes, be an integer and [Formula: see text] be a finite field of order [Formula: see text] with [Formula: see text]. We determine the weight enumerators of all irreducible cyclic codes of length [Formula: see text] over [Formula: see text] when multiplicative order of [Formula: see text] modulo [Formula: see text] is [Formula: see text]; [Formula: see text] and [Formula: see text]; [Formula: see text], where [Formula: see text].