Weight enumerators of all cubic-primitive irreducible cyclic codes of odd prime power length

Let p and q be odd primes and q be a cubic primitive modulo pu for some positive integer u. In this paper, we prove that the solutions of some Diophantine equations provide the weight enumerators of some cubic primitive irreducible cyclic codes of prime length. Bounds on the minimum distances of these codes are also given. (c) 2023 Elsevier Inc. All rights reserved.