�-cycles, S 2 -sets and Curves with Many Points

• Autores: Álvaro Garzón R.
• Localización: Revista de Ciencias Universidad del Valle, ISSN-e 2248-4000, ISSN 0121-1935, Vol. 21, Nº. 1, 2017
• Idioma: inglés
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• Resumen

  • Abstract We construct S 2-sets contained in the integer interval I q-1 = [1,q - 1] with q = 𝑝 n , 𝑝 a prime number and n ∈ Z+, by using the 𝑝-adic expansion of integers. Such sets come from considering 𝑝-cycles of length n. We give some criteria in particular cases which allow us to glue them to obtain good S 2-sets. After that we construct algebraic curves over the finite field 𝔽 q with many rational points via minimal (𝔽𝑝, 𝔽𝑝)-polynomials whose exponent set is an S 2-set.