The permutation and automorphism groups of univariate multiplicity codes

arXiv:2610.31858v1 Announce Type: new 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.