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Construction of binary Hadamard codes and their s-PD sets

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Abstract

This article presents the construction of binary linear Hadamard codes with parameters (2n,4n,n) over the fields F4 and F8. We generalize this construction to the field \(F_{2^{k}}\) to generate Hadamard codes with parameters \(\left (2^{k-1}n, 2^{k}n, 2^{k-2}n\right )\) for \(k\in \mathbb {N}\). We construct s-PD sets of size s + 1, a special subset of the permutation automorphism group of a code, which enables the correction of s errors for Hadamard codes over the field F4. We also discuss the decoding algorithm for these Hadamard codes.

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Acknowledgements

The authors are grateful to two anonymous reviewers for critically reading the manuscript and suggesting substantial improvements.

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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  1. Department of Mathematics, University of Mumbai, Mumbai, 400098, India

    Briji J. Chathely & Rajendra P. Deore

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  1. Briji J. Chathely
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Correspondence to Briji J. Chathely.

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Briji J. Chathely and Rajendra P. Deore declare that they have no conflict of interest.

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Chathely, B.J., Deore, R.P. Construction of binary Hadamard codes and their s-PD sets. Cryptogr. Commun. 13, 425–438 (2021). https://doi.org/10.1007/s12095-021-00471-5

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