# Coding Theory¶

## Basic Coding Theory objects¶

## Catalogs¶

## Code constructions¶

The named code families below are represented in Sage by their own classes, allowing specialised implementations of e.g. decoding or computation of properties:

In contrast, for some code families Sage can only construct their generator matrix and has no other a priori knowledge on them:

## Derived Code Constructions¶

Sage supports the following derived code constructions. If the constituent code is from a special code family, the derived codes inherit e.g. decoding or minimum distance capabilities:

Other derived constructions that simply produce the modified generator matrix can be found among the methods of a constructed code.

## Source coding¶

## Other modules¶

- Relative finite field extensions
- Guruswami-Sudan decoder for (Generalized) Reed-Solomon codes
- Interpolation algorithms for the Guruswami-Sudan decoder
- Guruswami-Sudan utility methods
- Information-set decoding for linear codes
- Bounds for Parameters of Codes
- Delsarte, a.k.a. Linear Programming (LP), upper bounds