有限域上自正交循环码的存在性

廖群英, 李雁彬, 廖欢

数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 117-124.

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PDF(466 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 117-124. DOI: 10.12386/A2014sxxb0011
论文

有限域上自正交循环码的存在性

    廖群英, 李雁彬, 廖欢
作者信息 +

The Existence for Self-Orthogonal Cyclic Codes over Finite Fields

    Qun Ying LIAO, Yan Bin LI, Huan LIAO
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文章历史 +

摘要

给出了非平凡自正交循环码和自对偶循环码存在的充要条件及其计数公式,并由此得到几类非平凡自正交循环码存在性的一个简便易行的判别方法.

Abstract

We obtain a necessary and sufficient condition for that there exists a nontrivial self-orthogonal or self-dual cyclic codes over finite fields and the explicit enumerating formula. As a corollary, a simple and easy criterion for several classes of non-trivial self-orthogonal cyclic codes is given.

关键词

循环码 / 自正交码 / 自对偶码 / 反向多项式

Key words

cyclic code / self-orthogonal code / self-dual code / reciprocal polynomial

引用本文

导出引用
廖群英, 李雁彬, 廖欢. 有限域上自正交循环码的存在性. 数学学报, 2014, 57(1): 117-124 https://doi.org/10.12386/A2014sxxb0011
Qun Ying LIAO, Yan Bin LI, Huan LIAO. The Existence for Self-Orthogonal Cyclic Codes over Finite Fields. Acta Mathematica Sinica, Chinese Series, 2014, 57(1): 117-124 https://doi.org/10.12386/A2014sxxb0011

参考文献

[1] Feng K. Q., Algebraic Theory of Error-Correcting Codes (in Chinese), Tsinghua University Press, Beijing, 2005.
[2] Guenda K., Gulliver T., Self-dual repeated root cyclic and negacyclic codes over finite fields, Information Theory Proceedings (ISIT), 2012 IEEE International Symposium, 1994, 126: 391-393.
[3] Huffman W., Pless V., Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003.
[4] Jia Y., Ling S., Xing C. P., On self-dual cyclic codes over finite fields, IEEE Trans. Inform. Theory, 2011, 57(4): 2243-2251.
[5] Kai X., Zhu S., On cyclic self-dual codes, AAECC, 2008, 19: 509-525.
[6] Massey J., Reversible codes, Information and Control, 1964, 7(3): 369-380.
[7] Nedeloaia C., Weight distributions of cyclic self-dual codes, IEEE Trans. Inform. Theory, 2003, 49: 1582- 1591.
[8] Sarami C., A Mass Formula for Cyclic Self-Orthogonal Codes, The Proceedings of the 2007 International Conference on Foundations of Computer Science (FCS.07), Las Vegas, NV., http://faculty.uncfsu.edu/csarami/.

基金

国家自然科学基金重大项目(10990011);教育部博士点专项基金(20095134120001);四川省杰出青年学术技术带头人培育计划(2011JQ0037)
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