florath / covering-codes

A machine readable collection of known Covering Codes

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Covering Codes

Introduction

This repository contains a collection of results of Covering Codes. It tries to be as complete as possible and also lists historical results. A special case of this problem is the Football Pools Problem.

This is IMHO the first try to systematically collect the results in a machine readable form.

Problem Description

"In coding theory, a covering code is a set of elements (called codewords) in a space, with the property that every element of the space is within a fixed distance of some codeword."

https://en.wikipedia.org/wiki/Covering_code

Results

Each result is placed in a yaml file. It is noted if it is a solution, an upper bound or a lower bound.

The results directory contains the results with the following sorting:

results/q/R/n

where q is the alphabet size, R is the maximal distance, and n is the size (dimension).

Motivation

During my mathematics and computer science studies in the 1990 I first got in contact with this topic. One of the first technical papers I ever read was the one from Willes which was in a seminar to a computer science course. My thesis was about Simulated Annealing where also this problem class was part of my studies.

I'm fascinated how fast a simple problem gets that big and complex that only very few results are known.

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A machine readable collection of known Covering Codes

License:Apache License 2.0


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Language:C++ 94.1%Language:Makefile 3.0%Language:M4 2.7%Language:Shell 0.2%