Trace codes over Z_4, and Boolean functions

Shi Minjia; Liu Yan; Randriam Hugues; Sok Lin; Sole Patrick

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Trace codes over Z_4, and Boolean functions

机译：z_4和布尔函数的跟踪代码

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We construct trace codes over Z4 based on Boolean functions and their support. The Lee weight distribution of these codes is studied by using the Walsh-Hadamard transform of the Boolean functions, and exponential character sums. We obtain few weights codes. In particular, bent and semi-bent functions give three-weight codes.

机译：基于布尔函数及其支持，我们通过Z4构造跟踪代码。通过使用布尔函数的Walsh-Hadamard转换和指数字符和，研究了这些代码的Lee重量分布。我们获得了一些重量代码。特别地，弯曲和半弯曲的功能提供三重代码。

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来源
《Designs, Codes and Crytography》 |2019年第6期|1447-1455|共9页
作者
Shi Minjia; Liu Yan; Randriam Hugues; Sok Lin; Sole Patrick;
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作者单位

Anhui Univ Minist Educ Key Lab Intelligent Comp Signal Proc 3 Feixi Rd Hefei 230039 Anhui Peoples R China|Anhui Univ Sch Math Sci Hefei 230601 Anhui Peoples R China;

Anhui Univ Sch Math Sci Hefei 230601 Anhui Peoples R China;

Telecom ParisTech LTCI 46 Rue Barrault F-75013 Paris France;

Anhui Univ Sch Math Sci Hefei 230601 Anhui Peoples R China|Royal Univ Phnom Penh Dept Math Phnom Penh 12156 Cambodia;

Univ Paris 08 CNRS LAGA 2 Rue Liberte F-93526 St Denis Reunion France;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Galois rings; Boolean functions; Character sums;

机译：Galois戒指;布尔函数;字符总和;

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专利

1. Trace codes over Z_4, and Boolean functions [J] . Shi Minjia, Liu Yan, Randriam Hugues, Designs, Codes and Crytography . 2019,第6期

机译：Z_4上的跟踪代码和布尔函数
2. A study of cyclic and constacyclic codes over Z_4 + uZ_4 + υZ_4 [J] . Habibul Islam, Om Prakash International journal of information and coding theory . 2018,第2期

机译：关于Z_4 + uZ_4 +υZ_4上的循环和恒定循环码的研究
3. On the Construction of Some Type Ⅱ Codes over Z_4 x Z_4 [J] . EDERLINA G. NOCON Designs, Codes and Crytography . 2003,第3期

机译：关于Z_4 x Z_4上某些Ⅱ型码的构造
4. New Classes of Generalized Boolean Bent Functions Over Z_4 [C] . Nian Li, Xiaohu Tang, Tor Helleseth IEEE International Symposium on Information Theory . 2012

机译：通过Z_4的新一类广义布尔弯曲功能
5. Algorithmic and complexity results for Boolean and pseudo-Boolean functions. [D] . Gruber, Aritanan G. 2015

机译：布尔和伪布尔函数的算法和复杂度结果。
6. Single Neurons in CA1 Hippocampus Encode Trace Interval Duration during Trace Heart Rate (Fear) Conditioning in Rabbit [O] . Matthew D. McEchron, Wilbur Tseng, John F. Disterhoft 2003

机译：CA1海马中的单个神经元编码兔的跟踪心率（恐惧）调节过程中的跟踪间隔持续时间
7. Nonadditive Quantum Codes from $Z_4$-Codes [O] . Ling San, Solé Patrick 2008

机译：来自$ Z_4 $ -Codes的非可加量子码

Trace codes over Z_4, and Boolean functions

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