Weight enumerators of all irreducible cyclic codes of length n.

Let n = p 1 α 1 p 2 α 2 ... p r α r p r + 1 α r + 1 ... p v α v , where p 1 , p 2 , ... , p v are distinct odd primes, be an integer and F q be a finite field of order q with gcd (q , n) = 1. We determine the weight enumerators of all irreducible cyclic codes of length n over F q when multiplicative order of q modulo p i α i is p i β i ; 1 ≤ i ≤ r and 2 p i β i ; r + 1 ≤ i ≤ v , where 0 ≤ β i ≤ α i − 1. [ABSTRACT FROM AUTHOR]