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Programming language: Haskell
License: GNU General Public License v3.0 only
Tags: Math     Linear    
Latest version: v0.2.0
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README

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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