Complete Weight Enumerators of a Class of Linear Codes From Weil Sums

IEEE Access ◽

10.1109/access.2020.3034110 ◽

2020 ◽

Vol 8 ◽

pp. 194631-194639

Author(s):

Shudi Yang

Keyword(s):

Linear Codes ◽

Weight Enumerators ◽

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Complete weight enumerators of linear codes based on Weil sums

IEEE Communications Letters ◽

10.1109/lcomm.2020.3027754 ◽

2020 ◽

pp. 1-1

Author(s):

Shudi Yang

Keyword(s):

Linear Codes ◽

Weight Enumerators ◽

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A class of three-weight linear codes and their complete weight enumerators

Cryptography and Communications ◽

10.1007/s12095-016-0187-4 ◽

2016 ◽

Vol 9 (1) ◽

pp. 133-149 ◽

Author(s):

Shudi Yang ◽

Zheng-An Yao ◽

Chang-An Zhao

Keyword(s):

Linear Codes ◽

Weight Enumerators

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Complete weight enumerators of some linear codes and their applications

Designs Codes and Cryptography ◽

10.1007/s10623-015-0136-9 ◽

2015 ◽

Vol 81 (1) ◽

pp. 153-168 ◽

Author(s):

Chengju Li ◽

Sunghan Bae ◽

Jaehyun Ahn ◽

Shudi Yang ◽

Zheng-An Yao

Keyword(s):

Linear Codes ◽

Weight Enumerators

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Complete weight enumerators of a family of three-weight linear codes

Designs Codes and Cryptography ◽

10.1007/s10623-016-0191-x ◽

2016 ◽

Vol 82 (3) ◽

pp. 663-674 ◽

Author(s):

Shudi Yang ◽

Zheng-An Yao

Keyword(s):

Linear Codes ◽

Weight Enumerators

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A class of linear codes and their complete weight enumerators

Advances in Mathematics of Communications ◽

10.3934/amc.2020044 ◽

2021 ◽

Vol 15 (1) ◽

pp. 73-97

Author(s):

Dandan Wang ◽

◽

Xiwang Cao ◽

Gaojun Luo ◽

Keyword(s):

Linear Codes ◽

Weight Enumerators

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Complete weight enumerators of a class of linear codes

Discrete Mathematics ◽

10.1016/j.disc.2016.11.029 ◽

2017 ◽

Vol 340 (4) ◽

pp. 729-739 ◽

Author(s):

Shudi Yang ◽

Zheng-An Yao

Keyword(s):

Linear Codes ◽

Weight Enumerators

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A construction of linear codes and their complete weight enumerators

Finite Fields and Their Applications ◽

10.1016/j.ffa.2017.08.001 ◽

2017 ◽

Vol 48 ◽

pp. 196-226 ◽

Author(s):

Shudi Yang ◽

Xiangli Kong ◽

Chunming Tang

Keyword(s):

Linear Codes ◽

Weight Enumerators

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Complete weight enumerators of two classes of linear codes

Discrete Mathematics ◽

10.1016/j.disc.2016.09.003 ◽

2017 ◽

Vol 340 (3) ◽

pp. 467-480 ◽

Author(s):

Qiuyan Wang ◽

Fei Li ◽

Kelan Ding ◽

Dongdai Lin

Keyword(s):

Linear Codes ◽

Weight Enumerators

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Complete weight enumerators of some linear codes from quadratic forms

Cryptography and Communications ◽

10.1007/s12095-016-0190-9 ◽

2016 ◽

Vol 9 (1) ◽

pp. 151-163 ◽

Author(s):

Dan Zhang ◽

Cuiling Fan ◽

Daiyuan Peng ◽

Xiaohu Tang

Keyword(s):

Quadratic Forms ◽

Linear Codes ◽

Weight Enumerators

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Type IV codes over a non-unital ring

Journal of Algebra and Its Applications ◽

10.1142/s0219498822501420 ◽

2021 ◽

pp. 2250142

Author(s):

Adel Alahmadi ◽

Alaa Altassan ◽

Widyan Basaffar ◽

Hatoon Shoaib ◽

Alexis Bonnecaze ◽

...

Keyword(s):

Algebraic Structure ◽

Invariant Theory ◽

Linear Codes ◽

Hamming Weight ◽

Weight Enumerators ◽

Type Iv ◽

Commutative Local Ring ◽

There is a special local ring [Formula: see text] of order [Formula: see text] without identity for the multiplication, defined by [Formula: see text] We study the algebraic structure of linear codes over that non-commutative local ring, in particular their residue and torsion codes. We introduce the notion of quasi self-dual codes over [Formula: see text] and Type IV codes, that is quasi self-dual codes whose all codewords have even Hamming weight. We study the weight enumerators of these codes by means of invariant theory, and classify them in short lengths.

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