# An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture

## TL;DR

This paper establishes algebraic coding conditions that are both necessary and sufficient for the Maximum Distance Separable Conjecture, advancing understanding of optimal error-correcting codes.

## Contribution

It introduces a novel algebraic-coding framework that characterizes the MDS conjecture's validity with precise conditions.

## Key findings

- Derived algebraic conditions for MDS conjecture
- Provided necessary and sufficient criteria for MDS codes
- Enhanced theoretical understanding of error-correcting code optimality

## Abstract

In this paper, we provide Algebraic-Coding necessary and sufficient conditions for the Maximum Distance Separable Conjecture to hold.