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Extended Length and Error-Correcting-Capacity of First-Order Reed–Muller Code in Extended Length Range

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Abstract

In this paper all the parameters in the conditions of rather comparatively larger probability of the value of n, have been discussed. In this extended range \(\upmu\) < n \(\le\) \(4\upmu\), the relation between existence of vector v(S) having the lowest weight in the coset RMm + v(S), and different values of r and d, have been analyzed. The relation between the number (\(\tau\)) of vectors having lowest weight in RMm + v(S) and various values of n, r, and d have been analyzed; and the corresponding values of \(\tau\) have been found. Also, the number of vectors (t) with lowest weight d for various values of d depending upon different quantities constituting the values of n and µ, has been found, n lying in extended range. All this is aimed at analyzing and improving the error-correcting-capacity of Reed–Muller code (first-order). Efforts are made to discuss the validity of the extended length of code and error-correcting-capacity of such a code of increased length.

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Authors and Affiliations

  1. Department of Applied Sciences, Baba Farid College of Engineering and Technology, Bathinda, Punjab, India

    Balwinder Singh Brar

  2. Department of ECE, Yadavindra College of Engineering Punjabi University GKC, Talwandi Sabo, Bathinda, Punjab, India

    Jagtar Singh Sivia

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  1. Balwinder Singh Brar
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  2. Jagtar Singh Sivia
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Correspondence to Balwinder Singh Brar.

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Brar, B.S., Sivia, J.S. Extended Length and Error-Correcting-Capacity of First-Order Reed–Muller Code in Extended Length Range. Wireless Pers Commun 118, 2519–2537 (2021). https://doi.org/10.1007/s11277-021-08141-8

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