Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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LINEAR CODES DETECTING REPEATED $b$(FIXED) BURSTS OF UNEQUAL LENGTHS IN DISTINCT SUB-BLOCKS

Authors

  • Ritu Arora
  • Poonam Garg
  • Surbhi Madan

Keywords:

repeated burst of length $b$(fixed), parity check digits, linear combinations, syndrome, bounds.

DOI:

https://doi.org/10.17654/0974165823055

Abstract

Extensive use of data makes the reliability of a communication channel of great significance. Various types of errors and methods to control errors have been studied. In this paper, necessary and sufficient number of parity check digits required for a code to be able to detect a type of repeated burst, namely $b$(fixed) repeated burst, in two sub-blocks of varying lengths, have been obtained. The paper also presents an example of such a code.

Received: March 11, 2023
Accepted: July 3, 2023

References

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B. K. Dass, Poonam Garg and M. Zannetti, On repeated burst error detecting and correcting codes, Special Volume of East-West Journal of Mathematics, Contribution in General Algebra II (2008), 79-98.

B. K. Dass and Poonam Garg, On 2-repeated burst codes, Ratio Mathematica - Journal of Applied Mathematics 19 (2009), 11-24.

P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Laboratory, Mountain View, Calif., 1959.

R. W. Hamming, Error-detecting and error-correcting codes, Bell System Tech. J. 29 (1950), 147-160.

Shu Lin and Daniel J. Costello, Jr., Error Control Coding: Fundamentals and Applications, Princeton Hall, New Jersey, 1983.

W. W. Peterson and E. J. Weldon, Jr., Error-correcting Codes, 2nd ed., The MIT Press, Mass., 1972.

G. E. Sacks, Multiple error correction by means of parity-checks, IRE Trans. Inform. Theory 4 (1958), 145-147.

W. Cary Huffman and Vera Pless, Fundamentals of Error-correcting Codes, Cambridge University Press, 2003.

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Published

2023-07-21

Issue

Vol. 40 No. 1 (2023)

Section

Articles

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How to Cite

LINEAR CODES DETECTING REPEATED $b$(FIXED) BURSTS OF UNEQUAL LENGTHS IN DISTINCT SUB-BLOCKS. (2023). Advances and Applications in Discrete Mathematics, 40(1), 19-42. https://doi.org/10.17654/0974165823055

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