Near-MDS codes from elliptic curves

TL;DR

This paper introduces a novel method for constructing near-MDS codes using elliptic curves with a specific number of rational points, highlighting cases where these codes cannot be extended further.

Contribution

It presents a new construction of near-MDS codes from elliptic curves and analyzes their extendability properties.

Findings

Constructed near-MDS codes with parameters [n,9,n-9]_q from elliptic curves.

Identified cases where these codes cannot be extended to longer near-MDS codes.

Abstract

We provide a new construction of $[n,9,n-9]_q$ near-MDS codes arising from elliptic curves with $n$ ${\mathbb F}_q$-rational points. Furthermore we show that in some cases these codes cannot be extended to longer near-MDS codes.