Extensions of Hadamard Codes Defined on Rings

Abstract

In this study, some special matrices are constructed by choosing certain elements from finite rings and certain codes are written by using these matrices.These codes are extended to a field. Moreover these codes are classified and more good codes are written. 4  ring were obtained by Krotov D. in [1] and [2]. Hadamard Code over 4  in particular were worked by Krotov D. in [2]. We will deal with codes defined over finite rings and binary codes. Main aim is to obtain new and good codes. An n . rank square matrix M that total ingredient 1 or 1  where t MM nI  is defined Hadamard matrix. Hadamard codes are called a code defined by Hadamard matrices. It says that using Hadamard matrices new codes could be obtained.This study is a generalizations of results obtained in [7,8,9] for the finite chain rings over 2  .