Abstract
In this paper, we provide the degree distribution of irreducible factors of the composed polynomial f(L(x)) over \(\mathbb {F}_q\), where \(f(x)\in \mathbb {F}_q[x]\) is irreducible and \(L(x)\in \mathbb {F}_q[x]\) is a linearized polynomial. We further provide some applications of our main result, including lower bounds for the number of irreducible factors of f(L(x)), constructions of high degree irreducible polynomials and the explicit factorization of \(f(x^q-x)\) under certain conditions on f(x).
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Acknowledgements
This work was conducted during a visit to Carleton University, supported by the program CAPES-PDSE (process - 88881.134747/2016-01).
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Communicated by G. Kyureghyan.
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Reis, L. Factorization of a class of composed polynomials. Des. Codes Cryptogr. 87, 1657–1671 (2019). https://doi.org/10.1007/s10623-018-0568-0
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DOI: https://doi.org/10.1007/s10623-018-0568-0