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Generalized Cohn functions on Galois rings

장영호
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2020.06|한국수학논문집 (Korean Journal of Mathematics)|제28권 제2호|pp. 241-255

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참고문헌

키워드

Galois ringsFourier transformsDedekind determinant
주제분류수학

초록

Let ${\mathbb F}_q$ be the finite field with $q=p^m$ elements. A complex valued Cohn function defined on ${\mathbb F}_q$ is introduced in [1]. In this paper we define generalized Cohn functions on Galois rings and investigate their properties.

Abstract

Let ${\mathbb F}_q$ be the finite field with $q=p^m$ elements. A complex valued Cohn function defined on ${\mathbb F}_q$ is introduced in [1]. In this paper we define generalized Cohn functions on Galois rings and investigate their properties.

참고문헌 (9)

  1. T. Cochrane, "On a Problem of H. Cohn for Character Sums", Journal of Number Theory, 81, pp.120~129 (2000)
  2. 전상표, "The Gauss sums over Galois rings and its absolute values", 한국수학논문집, 26(3), pp.519~535 (2018), 강원경기수학회
  3. S. Lang, "Cyclotomic Fields" (1978), Springer-Verlag
  4. B. R. McDonald, "Finite Rings with Identity" (1974), Marcel Dekker
  5. A. A. Nechaev, "Kerdock code in a cyclic form", Discrete Math. Appl, 1, pp.365~384 (1991)
  6. F. Ozbudak, "Some constructions of systematic authentication codes using Galois rings", Des. Codes Cryptography, 41(3), pp.343~357 (2006)
  7. F. Shuqin, "Character sums over Galois rings and primitive polynomials over finite fields", Finite Fields and Their Applications, 10, pp.36~52 (2004)
  8. A. Terras, "Fourier Analysis on Finite Groups and Application" (1999), Cambridge Uni-versity Press
  9. Z. X. Wan, "Lectures on Finite Fields and Galois Rings" (2003), World Scientific

관련 논문AI추천

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