A proper class for Hamming codes

[sagetrac-dlucas]

codes.HammingCode is not a constructor for a class, but a method which builds a generic linear code.

This ticket proposes a class implementation of Hamming codes, using the API introduced in #18099 which properly sets Hamming codes as a class. It also comes with a new generic encoder for codes built from a parity check matrix.

CC: @wdjoyner @ppurka @ClementPernet

Component: coding theory

Author: David Lucas

Branch/Commit: 2b6875a

Reviewer: Clément Pernet

Issue created by migration from https://trac.sagemath.org/ticket/19930

[sagetrac-dlucas]

Branch: u/dlucas/hamming_code

[sagetrac-dlucas]

comment:2

I pushed the patch, this is now open for review.

Alongside with the new classes, I also made the (very small) following changes:

• an isinstance test in codecan/autgroup_can_label.pyx was based on the old API and thus was only working with instances of class LinearCode. I changed it so it works now with any linear code, specific code families included.

• the method __cmp__ in AbstractLinearCode was quite useless (imho), so I removed it.

David

---

New commits:

25707e7	Cleaned up index of modules
4bb269a	Merge branch 'cleanup_index_coding' into hamming_code
c8c9cc9	Added a new encoder based on parity check matrix
23c12cb	New class for Hamming codes
c92e42c	Fixed broken doctests in codecan folder, and changed an old insinstance test
3b48dcb	Fixed broken doctests, removed `__cmp__` method

[sagetrac-dlucas]

Author: David Lucas

[sagetrac-dlucas]

Commit: 3b48dcb

[sagetrac-git]

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

a2177eb

Fixed import related to Hamming code in graphs/generators/smallgraphs.py

[sagetrac-git]

Changed commit from 3b48dcb to a2177eb

[sagetrac-git]

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

cc237db	Update to 7.1beta0
cc49f28	Added references for computation of parity check matrix in non-binary field

[sagetrac-git]

Changed commit from a2177eb to cc49f28

[sagetrac-dlucas]

comment:5

I updated this ticket to latest beta.
I also added a note on parity_check_matrix method which points to some references on how to build Hamming codes over anything else than a binary field, as this is definitely non-standard.

Also note that with this ticket, the implementation of codes.LinearCodeFromCheckMatrix can be improved so it does not rely on the dual code but on the encoder introduced here (which saves computation at construction time). See follow-up ticket #19975 for this issue.

---

New commits:

cc237db	Update to 7.1beta0
cc49f28	Added references for computation of parity check matrix in non-binary field

[sagetrac-git]

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

ca8396a

Updated to 7.1beta1 and fixed merge conflict