Abstract
Brawley and Carlitz introduced the method of composed products in order to construct irreducible polynomials of large degree from polynomials of lower degree. A basic ingredient of their construction is a binary operation on a subset \(G \subseteq {\bar{\mathbb{F }}_{q}}\) having certain properties. In this paper we classify all such binary operations when \(|G|= \infty \) (which is the most interesting case) and show that field addition and field multiplication are essentially the only such operations.
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The author was partly supported by Tübitak Proj. Nr. 111T234.
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Communicated by D. Panario.
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Stichtenoth, H. A note on composed products of polynomials over finite fields. Des. Codes Cryptogr. 73, 27–32 (2014). https://doi.org/10.1007/s10623-013-9808-5
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DOI: https://doi.org/10.1007/s10623-013-9808-5