Codes from A_m-invariant polynomials

2024/12/16 by Giacomo Micheli, Micheli, Giacomo, Vincenzo Pallozzi Lavorante +3
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cooperative Communication and Network Coding

paper · pdf · doi:10.48550/arxiv.2412.12005

Abstract

Let q be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on \mathbb F_q[x₁,…,x_m] 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.

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