The Hamming and Golay Number-Theoretic Transforms
A. J. A. Paschoal, R. M. Campello de Souza, H. M. de Oliveira
TL;DR
This paper introduces two novel number-theoretic transforms derived from perfect linear block codes, specifically Hamming and Golay codes, and explores their properties within finite fields.
Contribution
The paper presents the derivation of new transforms from perfect codes, expanding the set of tools available for finite field signal processing.
Findings
Properties of the Hamming number-theoretic transform are analyzed.
Properties of the Golay number-theoretic transform are analyzed.
New transforms are based on perfect codes, enriching coding theory applications.
Abstract
New number-theoretic transforms are derived from known linear block codes over finite fields. In particular, two new such transforms are built from perfect codes, namely the \textit {Hamming number-theoretic transform} and the \textit {Golay number-theoretic transform}. A few properties of these new transforms are presented.
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