The permutation and automorphism groups of univariate multiplicity codes
Abstract
We give explicit characterizations of the permutations and linear isometries that leave (univariate) multiplicity codes invariant. We consider any evaluation subset of the finite field, any multiplicity and dimension, and the automorphisms are with respect to the Niederreiter-Rosenblom-Tsfasman (NRT) metric. For multiplicity one, we recover the permutation and automorphism groups of classical Reed--Solomon codes in the classical Hamming metric. In the main dimension range, automorphisms are uniquely determined by a projectivity that permutes the evaluation subset, up to multiplication by a nonzero scalar. For multiplicity one, permutations are given by affine maps that permute the evaluation subset. In contrast, for multiplicity at least two, permutations are only given by translations that permute the evaluation subset. Finally, we give an algebraic characterization of automorphisms of multiplicity codes for the folded Hamming metric.
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BibTeX
@misc{moreno2026permutation,
title = {{The permutation and automorphism groups of univariate multiplicity codes}},
author = {Eduardo Camps Moreno and Hiram H. López and Umberto Martínez-Peñas and Rodrigo San-José},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31858},
eprint = {2610.31858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31858},
}
RIS
TY - UNPB
TI - The permutation and automorphism groups of univariate multiplicity codes
AU - Eduardo Camps Moreno
AU - Hiram H. López
AU - Umberto Martínez-Peñas
AU - Rodrigo San-José
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31858
UR - https://arxiv.org/abs/2610.31858
AB - We give explicit characterizations of the permutations and linear isometries that leave (univariate) multiplicity codes invariant. We consider any evaluation subset of the finite field, any multiplicity and dimension, and the automorphisms are with respect to the Niederreiter-Rosenblom-Tsfasman (NRT) metric. For multiplicity one, we recover the permutation and automorphism groups of classical Reed--Solomon codes in the classical Hamming metric. In the main dimension range, automorphisms are uniquely determined by a projectivity that permutes the evaluation subset, up to multiplication by a nonzero scalar. For multiplicity one, permutations are given by affine maps that permute the evaluation subset. In contrast, for multiplicity at least two, permutations are only given by translations that permute the evaluation subset. Finally, we give an algebraic characterization of automorphisms of multiplicity codes for the folded Hamming metric.
ER -