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• W4386851071 endingPage "e1577" @default.
• W4386851071 startingPage "e1577" @default.
• W4386851071 abstract "This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all $4 times 4$ involutory maximum distance separable (MDS) matrices over $mathbf{F}_{2^m}$. The proposed method reduces the search space complexity at the level of $$sqrt n $$, where n represents the number of all $4 times 4$ invertible matrices over $mathbf{F}_{2^m}$ to be searched for. Hence, this enables us to generate all $4 times 4$ involutory MDS matrices over $mathbf{F}_{2^3}$ and $mathbf{F}_{2^4}$. After applying global optimization technique that supports higher Exclusive-OR (XOR) gates ( e.g ., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/non-involutory MDS matrices known over $mathbf{F}_{2^3}$, $mathbf{F}_{2^4}$ and $mathbf{F}_{2^8}$ in terms of XOR count. In this context, we present new $4 times 4$ involutory MDS matrices over $mathbf{F}_{2^3}$, $mathbf{F}_{2^4}$ and $mathbf{F}_{2^8}$, which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e ., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all $2^ktimes 2^k$ involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices." @default.
• W4386851071 created "2023-09-20" @default.
• W4386851071 creator A5005506642 @default.
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• W4386851071 date "2023-09-19" @default.
• W4386851071 modified "2023-10-14" @default.
• W4386851071 title "A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions" @default.
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• W4386851071 doi "https://doi.org/10.7717/peerj-cs.1577" @default.
• W4386851071 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/37810342" @default.
• W4386851071 hasPublicationYear "2023" @default.
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