Nader H. Bshouty, Nuha Diab, Shada R. Kawar, Robert J. Shahla, "Enumerating all the Irreducible Polynomials over Finite Field," WSEAS Transactions on Computers, vol. 15, pp. 248-257, 2016, DOI:
Nader H. Bshouty, Nuha Diab, Shada R. Kawar, Robert J. Shahla. Enumerating all the Irreducible Polynomials over Finite Field.
WSEAS Transactions on Computers. 2016;15:248-257.
WSEAS Transactions on Computers
Print ISSN: 1109-2750, E-ISSN: 2224-2872
Volume 15, 2016
Enumerating all the Irreducible Polynomials over Finite Field
Authors: , , ,
Abstract: In this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree n over a finite field and their roots in the extension field in quasilinear time cost per element. Our algorithm is based on an improved algorithm for enumerating all the Lyndon words of length n in linear delay time and the known reduction of Lyndon words to irreducible polynomials.
Pages: 248-257 WSEAS Transactions on Computers, ISSN / E-ISSN: 1109-2750 / 2224-2872, Volume 15, 2016, Art. #23 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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