Recurrent Methods for Constructing Irreducible Polynomials over GF(2s)

Authors:
Mels K. Kyuregyan
Affiliations:
Institute for Informatics and Automation Problems, Armenian National Academy of Sciences, P. Sevak str. 1, 375044, Yerevan, Armeniaf1kyuregm@forof.sci.amf1
Venue:
Finite Fields and Their Applications
Year:
2002

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Abstract

The paper is devoted to some results concerning the constructive theory of the synthesis of irreducible polynomials over Galois fields GF(q), q=2^s. New methods for the construction of irreducible polynomials of higher degree over GF(q) from a given one are worked out. The complexity of calculations does not exceed O(n^3) single operations, where n denotes the degree of the given irreducible polynomial. Furthermore, a recurrent method for constructing irreducible (including self-reciprocal) polynomials over finite fields of even characteristic is proposed.