Rewriting introductory thematic tutorial on coding theory

[sagetrac-dlucas]

With all the recent work done on the coding theory library in Sage, the existing thematic tutorial on CT should be updated.

This tutorial has (imho) some problems:

• it is more a catalog of available methods and constructions rather than an actual tutorial
• it goes very fast into very specific methods and details, which should not be mentioned here

This ticket proposes a complete rework of this tutorial, which, instead of listing methods and constructions, gives some clues on how to build generic linear codes and perform standard operations (encoding, decoding, adding errors in words) for people working on coding theory.
It also explains to the user how to find any method and construction he needs.
Furthermore, it keeps things simple and never goes into technical details, or advanced scientific notions, preferring in that case to redirect the interested reader to manual pages instead.

CC: @tscrim

Component: coding theory

Author: David Lucas

Branch: 12bf512

Reviewer: Julian Rueth

Issue created by migration from https://trac.sagemath.org/ticket/19897

[sagetrac-dlucas]

Branch: u/dlucas/introductory_thematic_tutorial

[sagetrac-dlucas]

Commit: 2057fee

[sagetrac-dlucas]

comment:2

I pushed my work, this is now open for review.

As a note for the reviewer/interested reader:

• I had to add a flag .. nodoctest at the beginning of the file, in order to not having to recreate a new object (code, channel) at the beginning of each code block. If one knows of to transfer created objects from one block to another (if possible), it would of course be better!

• New decoders New decoders for Generalized Reed-Solomon codes #19653 will introduce have interesting properties wrt their message space. I made this ticket a dependency of New decoders for Generalized Reed-Solomon codes #19653 and created a new paragraph related to decoders and message spaces in New decoders for Generalized Reed-Solomon codes #19653.

[sagetrac-dlucas]

Author: David Lucas

[jdemeyer]

comment:3

Replying to @sagetrac-dlucas:

If one knows of to transfer created objects from one block to another (if possible), it would of course be better!

See link and linkall

http://doc.sagemath.org/html/en/developer/coding_basics.html#testing-rest-documentation

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d9bcb28	Update to 7.1beta0
70e5211	Added ..linkall keyword and wrote a new paragraph on decoders and introspections

[sagetrac-git]

Changed commit from 2057fee to 70e5211

[sagetrac-dlucas]

comment:5

Thank you!

I put .. linkall at the beginning of the file.
I also updated a bit this tutorial by adding a new paragraph on decoders and introspection.
Reopening this for review.

David