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

[ gpl, library, math ] [ Propose Tags ]

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


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Versions [faq] 0.1.0, 0.1.1, 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 Thu Aug 30 19:21:29 UTC 2018
Distributions NixOS:0.2.0
Downloads 399 total (60 in the last 30 days)
Rating 2.0 (votes: 1) [estimated by rule of succession]
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Readme for linear-code-0.2.0

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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