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Pré-Publication, Document De Travail Année : 2024

Reed-Muller codes in the sum-rank metric

Résumé

We introduce the sum-rank metric analogue of Reed-Muller codes, which we called linearized Reed-Muller codes, using multivariate Ore polynomials. We study the parameters of these codes, compute their dimension and give a lower bound for their minimum distance. Our codes exhibit quite good parameters, respecting a similar bound to Reed-Muller codes in the Hamming metric. Finally, we also show that many of the newly introduced linearized Reed--Muller codes can be embedded in some linearized Algebraic Geometry codes, a property which could turn out to be useful in light of decoding.
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hal-04577005 , version 1 (15-05-2024)

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  • HAL Id : hal-04577005 , version 1

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Elena Berardini, Xavier Caruso. Reed-Muller codes in the sum-rank metric. 2024. ⟨hal-04577005⟩
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