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