The Hamming and Golay Number-Theoretic Transforms | Zendy

Arquimedes J. A. Paschoal | Zendy; Ricardo Souza | Zendy; H. M. de Oliveira | Zendy

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The Hamming and Golay Number-Theoretic Transforms

Author(s) -

Arquimedes J. A. Paschoal,

Ricardo Souza,

H. M. de Oliveira

Publication year - 2018

Publication title -

anais de xxxvi simpósio brasileiro de telecomunicações e processamento de sinais

Language(s) - English

Resource type - Conference proceedings

DOI - 10.14209/sbrt.2018.1

Subject(s) - binary golay code , hamming code , hamming weight , hamming distance , mathematics , discrete mathematics , block code , linear code , ternary golay code , hamming(7,4) , finite field , algorithm , arithmetic , decoding methods

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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