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arXiv · 1602.05032

Enumerating all the Irreducible Polynomials over Finite Field

Nader H. Bshouty·Nuha Diab·Shada R. Kawar·Robert J. Shahla
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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 where $N=n^2$ is the size of the output.} 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.

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Nader H. Bshouty, Nuha Diab, Shada R. Kawar, Robert J. Shahla. 2016-02-16. Enumerating all the Irreducible Polynomials over Finite Field. https://arxiv.org/abs/1602.05032

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