Suzuki-invariant codes from the Suzuki curve

2014/11/23 by Abdulla Eid, Eid, Abdulla, Hilaf Hasson +6
Computer Science · Mathematics · #11G20 #94B27 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:11G20 #msc:94B27

paper · pdf · doi:10.48550/arxiv.1411.6215

openalex publication_date 2014/11/23 · arxiv created 2014/11/25 · arxiv updated 2014/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the Suzuki curve y^q + y = x^q₀(x^q + x) over the field with q = 2^2m+1 elements. The automorphism group of this curve is known to be the Suzuki group Sz(q) with q²(q-1)(q²+1) elements. We construct AG codes over \mathbbF_q⁴ from a Sz(q)-invariant divisor D, giving an explicit basis for the Riemann-Roch space L(ℓ D) for 0 < ℓ ≤ q²-1. These codes then have the full Suzuki group Sz(q) as their automorphism group. These families of codes have very good parameters and are explicitly constructed with information rate close to one. The dual codes of these families are of the same kind if 2g-1 ≤ ℓ ≤ q²-1.

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