Kuadratik Rezidülerden Fark Kümesi Oluşturma

Yıl 2023, Cilt: 39 Sayı: 2, 235 - 240, 31.08.2023

Emek Demirci Akarsu Yasin Yımaz

Öz

Fark kümeleri, alan teorisi, kombinatorik, sayılar teorisi ve kodlama teorisi gibi matematiğin alt alanlarıyla kesişen önemli cebirsel ifadelerdir. Diğer alanlarda da birçok uygulama alanına sahiptirler. Fark kümelerinin nasıl oluşturulacağı konunun en önemli kısmıdır. Bu makale, ikinci dereceden kalıntı sınıfları tarafından fark kümeleri üreten ve bunu alanlara uygulayan yeni bir yöntem, yani İkinci Dereceden Kalıntı Sınıfları Yöntemi (QRCM) önermektedir. Sonuçlar, QRCM'nin bir alan için ikinci dereceden kalıntı sınıfının bir fark kümesi olup olmadığını başarıyla belirlediğini göstermektedir.

Anahtar Kelimeler

Fark Kümeleri, İkinci dereceden rezidüler, QRCM Algoritması

Difference Sets from Quadratic Residues

Öz

Difference sets are significant algebraic objects that intersect a collection of sub-areas of mathematics, such as field theory, combinatorics, number theory, and coding theory. They also have lots of application areas in other fields. The essential part of the subject is how to construct difference sets. This article proposes a new method, i.e., the Quadratic Residue Classes Method (QRCM), which produces difference sets by quadratic residue classes, and applies it to fields. The results show that QRCM successfully determines whether the quadratic residue class for a field is a difference set.

Anahtar Kelimeler

Difference sets, Quadratic residues, QRCM Alghorithm

Kaynakça

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