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Anti-codes on solid burst of length $b$ of anti-weight $t$

CJM Vol. 7 (December 2015) [1], pp. 1 – 15.

Author(s): 
Pankaj Kumar Das [2]

Abstract: 

This paper considers a new kind of error which will be termed as `solid burst of length $b$ of anti-weight $t$'. Lower and upper bounds on the number of parity checks required for the existence of anti-codes that detect solid burst of length $b$ or less of anti-weight $t$ or more are obtained. This is followed by an example of such anti-codes. The paper also deals with anti-codes capable of detecting and simultaneously correcting such errors. Then the maximum anti-weight of such errors in the space of $n$-tuples is discussed. Further, the paper obtains an upper bound on the number of parity checks required for the existence of anti-codes that detect solid burst of length $b$ or less of anti-weight $t$ or more, together with $e$ or less random errors of anti-weight $t$ or more ($e < b$).

Keywords: 
Parity check matrix [3]
syndrome [4]
standard array [5]
coset [6]
solid burst error [7]

2010 Mathematics Subject Classification: 
94B05 [8]
94B20 [9]
94B65 [10]

Full Paper (PDF): 
AttachmentSize
PDF icon CJM2014-011-Yot.pdf [11]135.47 KB

Source URL: http://math.sc.chula.ac.th/cjm/content/anti-codes-solid-burst-length-b-anti-weight-t

Links
[1] http://www.math.sc.chula.ac.th/cjm/vol7
[2] http://math.sc.chula.ac.th/cjm/tags/pankaj-kumar-das
[3] http://math.sc.chula.ac.th/cjm/tags/parity-check-matrix
[4] http://math.sc.chula.ac.th/cjm/tags/syndrome
[5] http://math.sc.chula.ac.th/cjm/tags/standard-array
[6] http://math.sc.chula.ac.th/cjm/tags/coset
[7] http://math.sc.chula.ac.th/cjm/tags/solid-burst-error
[8] http://math.sc.chula.ac.th/cjm/tags/94b05
[9] http://math.sc.chula.ac.th/cjm/tags/94b20
[10] http://math.sc.chula.ac.th/cjm/tags/94b65
[11] https://d2ijd3g5wqapxj.cloudfront.net/cjm/sites/www.math.sc.chula.ac.th.cjm/files/CJM2014-011-Yot.pdf