Coding Theory Documentation Update

[gh-emes4]

With the changes to the coding theory framework (#28073, #28350) and new additions (#21226), some of the bigger documentation files need changing. These are the thematic tutorials on ​coding theory and ​creating a class in coding theory, as well as the ​linear code construction documentation. It might also be a good idea to add new tutorials on how to create a generic code/rank-metric code.

[dimpase]

reporters and commenters are cc'd automatically.

[jsrn]

This ticket should depend on #28073 and #21226, not the other way around. I.e. we first need to green-light #28073 and #21226, and then we can make some updates to the tutorials.

Regarding the documentation in the linear code class, we should update that already in #28073 or #21226 only if it is very misleading. Consider the state of SageMath if those two tickets were merged but this one wasn't: is the documentation in linear code then somewhat reasonable or completely wrong?

[gh-emes4]

The documentation in linear_code should be completely reasonable, I changed it along the way as I was working on AbstractCode. The only issue are the bigger documentation files - maybe it would be best to temporarily take them out of Sage before they are edited so they don't confuse anyone?

[dimpase]

Replying to gh-emes4:

The documentation in linear_code should be completely reasonable, I changed it along the way as I was working on AbstractCode. The only issue are the bigger documentation files - maybe it would be best to temporarily take them out of Sage before they are edited so they don't confuse anyone?

I think it's OK to have such inconsistencies as long as they don't make it into a stable release, which probably won't happen before Sept.

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​f7d9438	Merge in 28350, Linear Code No Metric
​d4d3e89	No Metric changes. Removed Relative Finite Field Extension, added vector_space method and basis option. Doctests and documentation. Deleted rank metric specific encoders.
​1e32a0c	Super method of LinearRankMetricCode includes basis.
​3917048	Merge branch 'develop' of git://trac.sagemath.org/sage into rank_metric
​01d9a3d	Merge branch 'develop' of git://trac.sagemath.org/sage into t/28350/abstract_linear_code_no_metric_class
​226ffbf	Added no metric to coding documentation index. Moved zero method from AbstractLinearCode. Changed base_field check.
​bd31704	Merge branch 'u/gh-emes4/coding/no_metric' of git://trac.sagemath.org/sage into rank_metric
​0a115d0	Removed zero method. Added field extension method.
​f6ab136	Documentation changes to coding module.
​a6d14cb	Thematic tutorials updated.

[gh-emes4]

I made necessary changes to the documentation in the coding module as well as some of the thematic tutorials.

For the thematic tutorials, I mostly tried to keep them as they were, correct things that were not relevant and add some new examples. I tried a few different things, but keeping in mind the audience for these tutorials, I decided to still keep the focus on linear codes over the Hamming metric.

In Coding Theory, I just added a new section explaining that there are other classes supporting codes which are not necessarily linear and/or over the Hamming metric, and added an example of a rank metric code.

In Structures in Coding Theory, I kept the main example of the repetition code throughout the tutorial. I added a section on the structure of the abstract classes in the beginning and also added a small example of a non-linear code family.