Restricted 2-Burst-Correcting Non-Binary Optimal Codes

By : Tarun Lata , Vinod Tyagi

Page No: 145-154

Abstract
Burst is the most common error in almost all communication channels and burst error correcting codes are developed to deal with such errors. According to Fire [7], a burst of length b or less is a vector whose all the non-zero components are confined to some b consecutive positions, the first and the last of which is non-zero. In this paper, we have introduced the idea of “restricted burst”, which is the modification of the definition of a burst. By a restricted burst of length b or less we mean a vector whose all the non-zero components are confined to some b consecutive positions, the first and last of which is nonzero with a restriction that all the non-zero consecutive positions contain same field element. For example in non-binary case for q = 3, n = 3 and b = 2, we have the following vectors of restricted burst of length 2 or less 110, 220, 011, 022, 100, 200, 010, 020, 001, 002. This idea may look hypothetical from practical point of view but we know it is true for binary case. Also the work may not have any practical utility at present but it is interesting from theoretical point of view. In this work, we present two construction techniques for optimal codes with respect to restricted burst of length 2 or less for linear as well as for byte oriented codes with redundancy r ?3.

Authors :
Vinod Tyagi : Department of Mathematics, Shyam Lal College (Evening), University of Delhi, Delhi-110032, India.
Tarun Lata : Research Scholar, Department of Mathematics, University of Delhi, Delhi-110007, India
 

DOI: Authors :