Reed-Muller codes in the sum-rank metric
<|reference_start|>Reed-Muller codes in the sum-rank metric: 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.<|reference_end|>
@article{berardini2024reed-muller,
    title={Reed-Muller codes in the sum-rank metric},
    author={Elena Berardini (UB, IMB, CANARI), Xavier Caruso (IMB, CANARI, UB)},
    journal={arXiv preprint arXiv:2405.09944},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.09944},
    primaryClass={cs.IT math.IT}
}