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- Title
On constacyclic codes of length 9ps over pm and their optimal codes.
- Authors
Dinh, Hai Q.; Ha, Hieu V.; Nguyen, Nhan T. V.; Tran, Nghia T. H.
- Abstract
The problem of classifying constacyclic codes over a finite field, both the Hamming distance and the algebraic structure, is an interesting problem in algebraic coding theory. For the repeated-root constacyclic codes of length n p s over p m , where p is a prime number and p does not divide n , the problem has been solved completely for all n ≤ 6 and partially for n = 7 , 8. In this paper, we solve the problem for n = 9 and all primes p different from 3 and 1 9. In particular, we characterize the Hamming distance of all repeated-root constacyclic codes of length 9 p s over p m . As an application, we identify all optimal and near-optimal codes with respect to the Singleton bound of these types, namely, MDS, almost-MDS, and near-MDS codes.
- Subjects
HAMMING distance; ALGEBRAIC coding theory; PRIME numbers; FINITE fields; CYCLIC codes
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498825500768