Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Embedding in MDS codes and Latin cubes

Vladimir N. Potapov

Abstract

An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $ρ$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and $n$-ary quasigroups.

Embedding in MDS codes and Latin cubes

Abstract

An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance and length can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and -ary quasigroups.

Paper Structure

This paper contains 4 sections, 10 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorem 1
  4. Embedding into Latin hypercube