A Generalized Construction and Improvements on Nonbinary Codes From Goppa Codes

Tomlinson M.; Jibril M.; Tjhai C.; Bezzateev S.V.

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A Generalized Construction and Improvements on Nonbinary Codes From Goppa Codes

机译：Goppa码对非二进制码的广义构造和改进

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摘要

We present an efficient construction of extended length Goppa codes. Using this construction, we obtain 78 new nonbinary codes with better minimum distance than the previously known codes with the same length and dimension. The construction is based on the observation that certain Goppa codes can be seen as BCH codes.

机译：我们提出了扩展长度的Goppa码的有效构造。使用这种结构，我们获得了78个新的非二进制代码，其最小距离比以前已知的具有相同长度和尺寸的代码更好。该构造是基于观察到的，某些Goppa码可被视为BCH码。

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《IEEE Transactions on Information Theory》 |2013年第11期|7299-7304|共6页
作者
Tomlinson M.; Jibril M.; Tjhai C.; Bezzateev S.V.;
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作者单位

School of Computing and Mathematics, University Of Plymouth, United Kingdom, UK|c|;

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原文格式 PDF
正文语种 eng
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关键词
BCH; Goppa; Reed–Solomon; error correction;

机译：BCH;Goppa;里德-所罗门;纠错;

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专利

1. Using the Structure of Subfields in the Construction of Goppa Codes and Extended Goppa Codes [J] . Tomlinson Martin, Bezzateev Sergey V., Jibril Mubarak, Information Theory, IEEE Transactions on . 2015,第6期

机译：在Goppa码和扩展Goppa码的构造中使用子域的结构
2. A Generalized Construction of Extended Goppa Codes [J] . Jibril M., Bezzateev S.V., Tomlinson M., Information Theory, IEEE Transactions on . 2014,第9期

机译：扩展Goppa码的广义构造
3. Nonbinary Quantum Goppa Codes Exceeding the Quantum Gilbert-Varshamov Bound [J] . Annika Niehage Quantum Information Processing . 2007,第3期

机译：非二进制量子Goppa码超出量子Gilbert-Varshamov界
4. Equivalent Irreducible Goppa Codes and the Precise Number of Quintic Goppa Codes of Length 32 [C] . John A. Ryan, Kondwani Magamba IEEE South Aftica Conference . 2007

机译：等效的不可挽回的GOPPA代码和长度为32的精确数量
5. On towers of function fields and the construction of the corresponding Goppa codes. [D] . Shor, Caleb McKinley. 2005

机译：在功能字段的塔上以及相应的Goppa规则的构造。
6. Semidefinite bounds for nonbinary codes based on quadruples [O] . Bart Litjens, Sven Polak, Alexander Schrijver -1

机译：基于四倍的非二进制代码的半定界
7. On the Cyclicity of Goppa Codes, Parity-Check Subcodes of Goppa Codes, and Extended Goppa Codes [O] . Berger Thierry P. 2000

机译：关于Goppa码的循环性，Goppa码的奇偶校验子码和扩展Goppa码
8. The Construction of Nonbinary Correcting Arithmetic Codes [R] . Tereshchenko, V. S. 1970

机译：非二元校正算术码的构造

A Generalized Construction and Improvements on Nonbinary Codes From Goppa Codes

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