Weight distributions of some irreducible cyclic codes of length n

Let n = p 1 α 1 p 2 α 2 . . . p r α r , where p i ’s are distinct odd primes, be a positive integer and F l be a finite field of prime order l where g c d ( l , n ) = 1 . Here, we compute the weight distributions of all irreducible cyclic codes of length n over F l for the case when multiplicative order of l modulo p i α i ; O p i α i ( l ) : = 2 p i α i - 1 for each α i ≥ 1 . It is also shown that computation of weight distributions of irreducible cyclic codes of length p 1 p 2 . . . p r over F l is sufficient to compute the weight distributions of all irreducible cyclic codes of length n .