QA616 : Study of special cyclic codes over non-commutative rings
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2021
Authors:
[Author], Abdollah Alhevaz[Supervisor], Ebrahim Hashemi[Advisor]
Abstarct: In this thesis, we study skew-cyclic codes over skew-polynomial rings of automorphism type. Skew-polynomial rings have been introduced and discussed by Ore (1933), and they are one of the important classes of non-commutative rings. Evaluation of skew polynomials and sets of (right) roots were first considered by Lam (1986) and studied in great detail by Lam and Leroy thereafter. After a detailed presentation of the most relevant properties of skew polynomials, we study algebraic theory of skew-cyclic codes as introduced by Boucher and Ulmer (2007) and studied by many authors thereafter. Skew-circulant matrices playing explosion role in this study. Finally, skew-cyclic codes with designed minimum distance are discussed, and we study two different kinds of skew-BCH codes, which were designed recently.
Keywords:
#cyclic code #skew polynomial ring #generator matrix #parity check matrix #generating polynomial #minimum distance design #BCH code #RS code. Keeping place: Central Library of Shahrood University
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