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Designs, Codes and Cryptography

Erschienen in:

09.10.2018

Factorization of a class of composed polynomials

verfasst von: Lucas Reis

Erschienen in: Designs, Codes and Cryptography | Ausgabe 7/2019

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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).

Vorheriger Artikel Erasure combinatorial batch codes based on nonadaptive group testing

Nächster Artikel Equiangular tight frames from group divisible designs

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Titel: Factorization of a class of composed polynomials
verfasst von: Lucas Reis
Publikationsdatum: 09.10.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 7/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0568-0

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