Enumerating all the Irreducible Polynomials over Finite Field
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2016
- DOI:
- 10.48550/arXiv.1602.05032
- arXiv:
- arXiv:1602.05032
- Bibcode:
- 2016arXiv160205032B
- Keywords:
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- Computer Science - Discrete Mathematics