Author:
Kyureghyan Gohar M.,Kyureghyan Melsik K.
Abstract
AbstractIn this paper we consider in detail the composition of an irreducible polynomial with $$X^2$$X2 and suggest a recurrent construction of irreducible polynomials of fixed degree over finite fields of odd characteristics. More precisely, given an irreducible polynomial of degree n and order $$2^rt$$2rt with t odd, the construction produces $$ord_t(2)$$ordt(2) irreducible polynomials of degree n and order t. The construction can be used for example to search irreducible polynomials with specific requirements on its coefficients.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory
Reference13 articles.
1. Berlekamp, E.: Algebraic Coding Theory. Worls Scientific Publ. Co. Pte. Ltd., Singapore (2015)
2. Brochero Martìnez, F.E., Reis, L., Silva, L.: Factorization of Composed Polynomials and Applications. arXiv:1901.02951
3. Carlitz, L.: Distribution of primitive roots in a finite field. Q. J. Math. Oxf. Ser. (2) 4(1), 4–10 (1953)
4. Cohen, S.D.: The explicit construction of irreducible polynomials over finite fields. Des. Codes Cryptogr. 2, 169–173 (1992)
5. Cohen, S.D., Kapetanakis, G.: Finite Field Extensions with the Line or Translate Property for $r$-Primitive Elements. arXiv:1906.08046
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