Explicit factorization of x1lm1l2m2l3m3 - a and a-constacyclic codes over a finite field

Let F-q be a finite field of order q, t be a prime and m(1), m(2), m(3) be positive integers. In this article, we find all irreducible divisors of x(1)(lm1l2m2l3m3) - a over F-q where a is an element of F-q* and q(t) - 1 = l(1)(V1)l(2)(V2)l(3)(V3) c such that l(1), l(2), l(3) are distinct odd primes and c is a positive integer with gcd(l(1) l(2) l(3), c) = 1 and gcd(l(1)l(2)l(3), q(q - 1)) = 1. Moreover, we construct an a-constacyclic code by using these irreducible divisors.