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On the construction of irreducible and primitive polynomials from [formula omitted] to [formula omitted].
- Source :
-
Finite Fields & Their Applications . Feb2022, Vol. 78, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- In this paper, we present two constructions of irreducible (primitive) polynomials over F q of degree rm from irreducible (primitive) polynomial over F q m of degree r , and we show that these two constructions coincide. The first construction is based on the Frobenius automorphism of F q m over F q. The second one comes from a generalization of a construction of primitive polynomials over F q which uses the companion matrix. From this generalization, given an irreducible (resp. primitive) polynomial over F q m of degree r , we generate multiple (resp. all) irreducible polynomials over F q of degree rm. As an application, a characterization of the generator polynomial of a BCH code over F q is given. Then, we show how two BCH codes over F q and F q m , respectively, and their generator polynomials are related. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 78
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 154298406
- Full Text :
- https://doi.org/10.1016/j.ffa.2021.101971