A note on composed products of polynomials over finite fields
Stichtenoth, Henning (2014) A note on composed products of polynomials over finite fields. Designs, Codes, and Cryptography, 73 (1). pp. 27-32. ISSN 0925-1022 (Print) 1573-7586 (Online)
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Official URL: http://dx.doi.org/10.1007/s10623-013-9808-5
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⊆Fˉq having certain properties. In this paper we classify all such binary operations when |G|=∞ (which is the most interesting case) and show that field addition and field multiplication are essentially the only such operations.
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