On Cyclic Codes Over Finite Chain Rings and Self-Dual Cyclic Codes Over Finite Fields

Abstract

Theorems in coding theory has extended from fields Fq to finite chain rings R. In this thesis, we introduce the structure of R and properties over R, discuss theorems for codes C over R, talk about self-dual cyclic codes over finite fields Fq, and give examples for codes over R and Fq.Theorems in coding theory has extended from fields Fq to finite chain rings R. In this thesis, we introduce the structure of R and properties over R, discuss theorems for codes C over R, talk about self-dual cyclic codes over finite fields Fq, and give examples for codes over R and Fq.