SOME CLASSES OF LCD CODES AND SELF-ORTHOGONAL CODES OVER FINITE FIELDS

Li Xia; Cheng Feng; Tang Chunming; Zhou Zhengchun

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SOME CLASSES OF LCD CODES AND SELF-ORTHOGONAL CODES OVER FINITE FIELDS

机译：在有限字段上的一些液晶代码和自我正交代码

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Due to their important applications in theory and practice, linear complementary dual (LCD) codes and self-orthogonal codes have received much attention in the last decade. The objective of this paper is to extend a recent construction of binary LCD codes and self-orthogonal codes to the general p-ary case, where p is an odd prime. Based on the extended construction, several classes of p-ary linear codes are obtained. The characterizations of these linear codes to be LCD or self-orthogonal are derived. The duals of these linear codes are also studied. It turns out that the proposed linear codes are optimal in many cases in the sense that their parameters meet certain bounds on linear codes. The weight distributions of these linear codes are settled.

机译：由于理论和实践中的重要应用，线性互补双重（LCD）代码和自我正交代码在过去十年中受到了很多关注。本文的目的是将最近的二进制LCD代码和自我正交码构造到一般的P-ary案例，其中P是奇数的素数。基于扩展结构，获得了几类P-ary线性码。导出了这些线性码的特征是LCD或自正交的。还研究了这些线性码的双重。事实证明，在许多情况下，所提出的线性代码在许多情况下是最佳的，因为它们的参数在线性码上遇到某些界限。这些线性码的权重分布稳定。

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来源
《Advances in mathematics of communications》 |2019年第2期|共14页
作者
Li Xia; Cheng Feng; Tang Chunming; Zhou Zhengchun;
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作者单位

Southwest Jiaotong Univ Sch Math Chengdu 610031 Sichuan Peoples R China;

Southwest Jiaotong Univ Sch Math Chengdu 610031 Sichuan Peoples R China;

China West Normal Univ Sch Math &

Informat Nanchong 637002 Peoples R China;

Southwest Jiaotong Univ Sch Math Chengdu 610031 Sichuan Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Linear codes; self-orthogonal codes; LCD codes; weight distributions; Krawtchouck polynomial;

机译：线性码;自正交码;LCD代码;重量分布;克劳特堡多项式;

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专利

1. SOME CLASSES OF LCD CODES AND SELF-ORTHOGONAL CODES OVER FINITE FIELDS [J] . Li Xia, Cheng Feng, Tang Chunming, Advances in mathematics of communications . 2019,第2期

机译：在有限字段上的一些液晶代码和自我正交代码
2. LCD and Self-Orthogonal Group Codes in a Finite Abelian p -Group Algebra [J] . Li Fengwei, Yue Qin, Wu Yansheng IEEE Transactions on Information Theory . 2020,第5期

机译：LCD和自我正交组代码在有限的abelian p-group代数中
3. Enumeration formulae for self-dual, self-orthogonal and complementary-dual quasi-cyclic codes over finite fields [J] . Anuradha Sharma, Taranjot Kaur Cryptography and Communications . 2018,第3期

机译：有限域上自对偶，自正交和互补对偶准循环码的枚举公式
4. Classes of LDPC codes constructed from elements of finite fields and cyclotomic cosets [C] . Aly S.A., Mazaar H. Information Theory, 2009. CWIT 2009 . 2009

机译：LDPC码的类别，由有限域和环原子集构成
5. Construction and decoding of codes on finite fields and finite geometries. [D] . Zhang, Li. 2010

机译：有限域和有限几何上代码的构造和解码。
6. Source codes and simulation data for the finite element implementation of the conventional and localizing gradient damage methods in ABAQUS [O] . Subrato Sarkar, I.V. Singh, B.K. Mishra, 2019

机译：ABAQUS中常规和局部梯度损伤方法的有限元实现的源代码和仿真数据
7. Constructions of optimal LCD codes over large finite fields [O] . Sok, Lin, Shi, Minjia, Solé, Patrick 2017

机译：大型有限域上最优LCD码的构造
8. Self-Orthogonal Codes of Half Dimension Over GS(2) [R] . Pless, V. S. 1970

机译：Gs上的半维自正交码（2）

SOME CLASSES OF LCD CODES AND SELF-ORTHOGONAL CODES OVER FINITE FIELDS

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