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An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture

Steven B. Damelin, Daniel Kaiser, Jeffrey Sun, Safal Bora

Abstract

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

An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture

Abstract

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

Paper Structure

This paper contains 6 sections, 5 theorems, 9 equations.

Table of Contents

  1. Introduction: The MDS Conjecture
  2. Some known work on the MDS Conjecture
  3. Statement of Main Result
  4. The Proof of Theorem 1.4
  5. Prerequisites to the proof of Theorem 1.4
  6. Proof of Theorem 1.4

Key Result

Theorem 1.2

Let k be an integer such that $2 \leq k \leq q = p^r,$ where p is prime and r is a positive integer. The MDS Conjecture is true whenever $k \leq 2p-2.$

Theorems & Definitions (9)

  • Conjecture 1.1
  • Theorem 1.2: S.Ball
  • Definition 1.3
  • Theorem 1.4
  • Definition 2.1
  • Lemma 2.2
  • Corollary 2.3
  • Lemma 2.4
  • proof