学习纠错码和相关的计算代数系统

过去的一年致力于IEEE 802.3bj的前向纠错编码模块(FEC)，发现可以把我的对偶综合工作扩展到FEC上，包括FEC的形式化验证和对偶综合。

这就导致了我需要学习纠错码，而相关的多项式环和有限域操作需要在计算代数系统上进行操作，这就导致了我需要学习计算代数系统。

常见的计算代数系统由Singular(www.singular.uni-kl.de)和GAP(www.gap-system.org)。

Singular被几个相关的工作使用，比如发表于FMCAD12的Formal Verification of Error Correcting Circuits Using Computational Algebraic Geometry。

不过Singular的用户支持很差，在他的用户论坛和邮件列表中问问题，很久都没有人回复。

而GAP则好得多，他的邮件列表非常活跃，并针对学习纠错吗给出了下列相关的学习资源

Dear Shen,

In GAP there is a share package called GUAVA which is used for computations in coding theory. There are also a couple of notes scattered around which to some extent give you examples of use of GAP for Algebraic Coding Theory.

Have 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 has section of constructing codes using GAP and SAGE.

See http://www.sagenb.org/pdf/en/reference/coding/coding.pdf
I found this book useful for general use of GAP:

5. The book Abstract Algebra with GAP: A Manual to be 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

其中我发现2尤其有用，不仅不仅给出了相关的代数背景知识，还有GAP在纠错码上的应用，所有章节都有GAP的例子