Z_2-Triple Cyclic Codes and Their Duals

Authors

  • Srinivasulu B Research scholar, Indian Institute of Technology Roorkee, India.
  • Maheshanand Bhaintwal Indian Institute of Technology Roorkee, Roorkee, India - 247667.

Keywords:

Triple cyclic codes, minimal spanning sets, dual codes.

Abstract

A Z2-triple cyclic code of block length (r, s, t) is a binary code of length r + s + t such that the code is partitioned into three parts of lengths r, s and t such that each part is invariant under the cyclic shifts of the coordinates. Such a code can be viewed as Z2[x]-submodules of Z_2[x]/<x^r-1>*Z_2[x]/<x^s-1>*Z_2[x]/<x^t-1>, in polynomial representation. In this paper, we determine the structure of these codes. We have obtained the form of the generators for such codes. Further, a minimal generating set for such codes is obtained. Also, we study the structure of the duals of these codes via the generators of the codes.

Author Biographies

  • Srinivasulu B, Research scholar, Indian Institute of Technology Roorkee, India.
    I am a Research scholar at Indian Institute of Technology Roorkee, India. Currently I am working in the area of algebraic coding theory under the supervision of Dr. Maheshanand Bhaintwal.
  • Maheshanand Bhaintwal, Indian Institute of Technology Roorkee, Roorkee, India - 247667.
    Dr. Maheshanand is an Associate Professor in IIT Roorkee. His current area of research is Coding theory.

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Published

2017-02-03

Issue

Vol. 10 No. 2: (January 2017)

Section

Coding Theory and Cryptology

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How to Cite

Z_2-Triple Cyclic Codes and Their Duals. (2017). European Journal of Pure and Applied Mathematics, 10(2), 392-409. https://www.ejpam.com/index.php/ejpam/article/view/2666