Learning error-Correcting codes and related computational algebra systems

The past year has been dedicated to the IEEE 802.3BJ Forward Error Correction coding Module (FEC), and found that my dual synthesis work can be extended to FEC, including the formal validation and dual synthesis of FEC.

This led me to the need to learn the error-correcting code, and the related polynomial ring and finite field operations need to operate on the computational algebra system, which led me to learn computational algebra systems.

The common computational algebra system consists of singular (www. Singularuni-kl.de) and Gap (www. Gap-system.org).

Singular is used by several related jobs, such as formal verification of Error correcting circuits using computational algebraic Geometry published in FMCAD12.

However, singular user support is poor, in his user forum and mailing list to ask questions, for a long time no one reply.

And Gap is much better, his mailing list is very active, and for learning error-correcting it gives the following related learning resources

Dear Shen,

In GAP there are a share package called guava which are used for computations in coding theory. There is also a couple of notes scattered around which to some extent give you examples the use of the GAP for algebraic Codin G theory.
Has a look at the following:
1. http://www.gap-system.org/Manuals/pkg/guava-3.12/htm/chap8.html
2. http://www.usna.edu/Users/math/wdj/_files/documents/book/node139.html
3. Http://www.math.cornell.edu/~web3360/eccbook2007.pdf

4. The book titled:selected unsolved problems in coding theory, also have section of constructing codes using GAP and SAGE .
See Http://www.sagenb.org/pdf/en/reference/coding/coding.pdf

I found this book useful the GAP:
5. The book is abstract Algebra with gap:a Manual-to is used with contemporary Abstract Algebra, 5th Edition by Julianne G. Rainbolt and Joseph A. Gallian
August 2003 is also useful. I found a copy here:http://college.cengage.com/mathematics/gallian/abstract_algebra/5e/shared/gap/gap_manual.pdf

I hope this helps.
Regards,

Bernardo

I found that 2 is particularly useful, not only to give the relevant algebraic background knowledge, as well as the application of gap in error correction code, all chapters have an example of gap

Learning error-Correcting codes and related computational algebra systems