Meta-ticket: enhancement of the coding theory part of Sage

[dlucas]

This ticket summarizes the work done in the ​ACTIS project.

The main goal of this project is to enhance the decoding part of Sage, doing the following:

• propose a new API to manage code families
• propose a new API to manage multiple encoders for a given code family (i.e multiple message spaces)
• propose a new API to manage multiple decoding algorithms for a given code family
• implement numerous code families, alongside their encoders and decoders

The following table gives a quick access to all tickets related to the project.

The Nature column gives the "type" of the ticket :

• Structure means it's a structural ticket, which does not require any knowledge in coding theory. It will be for tickets which introduce new mechanisms in the API.
• Cleanup means it's a ticket that refreshes old existing code of the coding library, and/or documentation. It does not require any knowledge in coding theory.
• Content means it adds new mathematical content (code families, decoding algorithms, ...) to Sage. Some knowledge on the topic might be useful for these tickets.
• Documentation means it's a ticket which adds some new documentation in the library. It does not require any particular knowledge in coding library, nor being familiar with our code.

Topic	Ticket number	Nature
Linear codes and category framework	#18150	Structure
Structure for code families	#18099	Structure
Encoding structure	#18376	Structure
Decoding structure	#18813	Structure
Better names in coding	#17973	Cleanup
Improve __contains__ method	#18607	Cleanup
Clean imports	#19315	Cleanup
Clean dual_code, __eq__ and removed debug traces	#19492	Cleanup
Generic impl. for __ne__	#19743	Cleanup
Clean-up index of modules	#19907	Cleanup
Non-guava impl. for covering_radius	#19913	Cleanup
Clean LinearCodeFromCheckMatrix	#19975	Cleanup
Experimenting on codes	#18269	Structure & Content
GRS codes and dedicated encoders	#18928	Content
New decoders for GRS codes	#19653	Content
Guruswami-Sudan list-decoding	#19666	Content
Lee O'Sullivan for Guruswami-Sudan	#19722	Content
Punctured code and dedicated encoder	#19422	Content
Q-ary symmetric channel	#19511	Content
Syndrome decoder is a nearest neighbor decoder	#19623	Content
A proper class for Hamming codes	#19930	Content
A class for subfield subcodes	#20039	Content
API thematic tutorial	#19745	Documentation
Introductory thematic tutorial	#19897	Documentation
Document decoder types	#20001	Documentation