Linear codes from Denniston maximal arcs

TL;DR

This paper constructs new linear codes from Denniston maximal arcs, achieving specific parameters and potentially larger minimum distances for certain small q values, advancing coding theory.

Contribution

It introduces a method to generate linear codes from Denniston maximal arcs with explicit parameters and improved minimum distances for some cases.

Findings

Codes with parameters [(√q-1)(q+1), 5, d]_q for q=2^{4n+2}

Asymptotic minimum distance approaches (√q-1)q-3√q as q increases

Potentially larger minimum distances for codes at q=16 and 32

Abstract

In this paper we construct functional codes from Denniston maximal arcs. For $q=2^{4n+2}$ we obtain linear codes with parameters $[(\sqrt{q}-1)(q+1),5,d]_q$ where $\lim_{q \to +\infty} d=(\sqrt{q}-1)q-3\sqrt{q}$. We also find for $q=16,32$ a number of linear codes which appear to have larger minimum distance with respect to the known codes with same length and dimension.