Codes from $A_m$-invariant polynomials
Information Theory
2024-12-17 v1 math.IT
Number Theory
Abstract
Let be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with Generalized Reed-Muller codes with similar parameters, our codes have the same asymptotic relative distance but a better rate. Our results follow from combinations of Galois theoretical methods with Weil-type bounds for the number of points of hypersurfaces over finite fields.
Cite
@article{arxiv.2412.12005,
title = {Codes from $A_m$-invariant polynomials},
author = {Giacomo Micheli and Vincenzo Pallozzi Lavorante and Phillip Waitkevich},
journal= {arXiv preprint arXiv:2412.12005},
year = {2024}
}
Comments
Accepted in Designs, Codes, and Cryptography