Journal
FINITE FIELDS AND THEIR APPLICATIONS
Volume 93, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ffa.2023.102334
Keywords
Cyclic code; Minimum distance; Weight enumerator; Weight distribution
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In this paper, we investigate cubic primitive irreducible cyclic codes and provide bounds on their minimum distances. We also demonstrate a connection between solutions of Diophantine equations and weight enumerators of these codes.
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.
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