linear-code: A simple library for linear codes (coding theory, error correction)

This is a package candidate release! Here you can preview how this package release will appear once published to the main package index (which can be accomplished via the 'maintain' link below). Please note that once a package has been published to the main package index it cannot be undone! Please consult the package uploading documentation for more information.

[maintain] [Publish]

Please see the README on GitHub at https://github.com/wchresta/linear-code#readme


[Skip to Readme]

Properties

Versions 0.1.0, 0.1.1, 0.2.0, 0.2.0
Change log ChangeLog.md
Dependencies base (>=4.10 && <5), containers, data-default, ghc-typelits-knownnat, ghc-typelits-natnormalise, HaskellForMaths, matrix-static, random, random-shuffle [details]
License GPL-3.0-only
Copyright 2018, Wanja Chresta
Author Wanja Chresta
Maintainer wanja dot hs at chrummibei dot ch
Category Math
Home page https://github.com/wchresta/linear-code#readme
Bug tracker https://github.com/wchresta/linear-code/issues
Source repo head: git clone https://github.com/wchresta/linear-code
Uploaded by wchresta at 2018-08-30T19:20:01Z

Modules

[Index] [Quick Jump]

Downloads

Maintainer's Corner

Package maintainers

For package maintainers and hackage trustees


Readme for linear-code-0.2.0

[back to package description]

Build Status Hackage Hackage Deps

linear-code

Library to handle linear codes from coding theory.

The library is designed to carry the most important bits of information in the type system while still keeping the types sane.

This library is based roughly on Introduction to Coding Theory by Yehuda Lindell

Usage example

Working with random codes

> :m + Math.Code.Linear System.Random
> :set -XDataKinds
> c <- randomIO :: IO (LinearCode 7 4 F5)
> c
[7,4]_5-Code
> generatorMatrix c
( 1 0 1 0 0 2 0 )
( 0 2 0 0 1 2 0 )
( 0 1 0 1 0 1 0 )
( 1 0 0 0 0 1 1 )
> e1 :: Vector 4 F5
( 1 0 0 0 )
> v = encode c e1
> v
( 1 0 1 0 0 2 0 )
> 2 ^* e4 :: Vector 7 F3
( 0 0 0 2 0 0 0 )
> vWithError = v + 2 ^* e4
> vWithError
( 1 0 1 2 0 2 0 )
> isCodeword c v
True
> isCodeword c vWithError
False
> decode c vWithError
Just ( 1 0 2 2 2 2 0 )

Notice, the returned vector is NOT the one without error. The reason for this is that a random code most likely does not have a distance >2 which would be needed to correct one error. Let's try with a hamming code

Correcting errors with hamming codes

> c = hamming :: BinaryCode 7 4
> generatorMatrix c
( 1 1 0 1 0 0 0 )
( 1 0 1 0 1 0 0 )
( 0 1 1 0 0 1 0 )
( 1 1 1 0 0 0 1 )
> v = encode c e2
> vWithError = v + e3
> Just v' = decode c vWithError
> v' == v
True