Advanced Study on Cyclic Codes Associated to Muffin Ideals over Quaternion Integer Ring ((-1,-1)/z_p )

Authors

  • Shaikh Javed Shafee Government Polytechnic, Hingoli, Maharashtra, India.
  • Arunkumar R. Patil Department of Mathematics, Shri Guru Gobind Singhji Institute of Engineering and Technology, Vishnupuri, Nanded, Maharashtra, India.

DOI:

https://doi.org/10.9734/bpi/tpmcs/v6/1455D

Keywords:

Cyclic codes, quaternion algebra, muffin ideal, Mannheim distance

Abstract

In this paper, we construct cyclic codes associated with Muffin ideals over quaternion integer rings-  where  is the finite field integers modulo odd prime p. We also find a generator matrix in standard form for these cyclic codes. Further we determine the Mannheim distance of these cyclic codes. In future we would like to determine the Grobner basis of the cyclic codes associated with muffin ideals.

Published

2021-02-27

How to Cite

Shaikh Javed Shafee, & Arunkumar R. Patil. (2021). Advanced Study on Cyclic Codes Associated to Muffin Ideals over Quaternion Integer Ring ((-1,-1)/z_p ). Theory and Practice of Mathematics and Computer Science Vol. 8, 97–105. https://doi.org/10.9734/bpi/tpmcs/v6/1455D

Issue

Theory and Practice of Mathematics and Computer Science Vol. 8

Section

Chapters