A mass formula for cyclic codes over Galois rings of characteristic p 3

Finite Fields and Their Applications ◽

10.1016/j.ffa.2018.04.005 ◽

2018 ◽

Vol 52 ◽

pp. 214-242 ◽

Cited By ~ 4

Author(s):

Boran Kim ◽

Yoonjin Lee

Keyword(s):

Mass Formula ◽

Cyclic Codes ◽

Galois Rings ◽

Characteristic P

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Mass Formula for Self-Dual Codes over Galois Rings GR(p3, r)

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v12i4.3565 ◽

2019 ◽

Vol 12 (4) ◽

pp. 1701-1716

Author(s):

Trilbe Lizann Espina Vasquez ◽

Gaudencio Jr. Cempron Petalcorin

Keyword(s):

Positive Integer ◽

Mass Formula ◽

Galois Ring ◽

The Self ◽

Galois Rings ◽

Dual Codes ◽

Characteristic P

Let $p$ be an odd prime and $r$ a positive integer. Let $\text{GR}(p^3,r)$ be the Galois ring of characteristic $p^3$ and cardinality $p^{3r}$. In this paper, we investigate the self-dual codes over $\text{GR}(p^3,r)$ and give a method to construct self-dual codes over this ring. We establish a mass formula for self-dual codes over $\text{GR}(p^3,r)$ and classify self-dual codes over $\text{GR}(p^3,2)$ of length 4 for $p=3,5$.

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Weight distribution of double cyclic codes over Galois rings

Designs Codes and Cryptography ◽

10.1007/s10623-021-00914-3 ◽

2021 ◽

Author(s):

Jian Gao ◽

Xiangrui Meng ◽

Fang-Wei Fu

Keyword(s):

Weight Distribution ◽

Cyclic Codes ◽

Galois Rings

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Enumeration and construction of additive cyclic codes over Galois rings

Discrete Mathematics ◽

10.1016/j.disc.2015.01.012 ◽

2015 ◽

Vol 338 (6) ◽

pp. 922-937 ◽

Cited By ~ 4

Author(s):

Yonglin Cao ◽

Jian Gao ◽

Fang-Wei Fu ◽

Yuan Cao

Keyword(s):

Cyclic Codes ◽

Galois Rings

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Skew quasi-cyclic codes over Galois rings

Designs Codes and Cryptography ◽

10.1007/s10623-011-9494-0 ◽

2011 ◽

Vol 62 (1) ◽

pp. 85-101 ◽

Cited By ~ 20

Author(s):

Maheshanand Bhaintwal

Keyword(s):

Cyclic Codes ◽

Galois Rings ◽

Quasi Cyclic Codes

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Skew cyclic and quasi-cyclic codes of arbitrary length over Galois rings

International Journal of Algebra ◽

10.12988/ija.2013.310100 ◽

2013 ◽

Vol 7 ◽

pp. 803-807 ◽

Cited By ~ 4

Author(s):

Mingzhong Wu

Keyword(s):

Cyclic Codes ◽

Galois Rings ◽

Arbitrary Length ◽

Quasi Cyclic Codes

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Lee weights of cyclic self-dual codes over Galois rings of characteristic p 2

Finite Fields and Their Applications ◽

10.1016/j.ffa.2016.11.015 ◽

2017 ◽

Vol 45 ◽

pp. 107-130 ◽

Cited By ~ 6

Author(s):

Boran Kim ◽

Yoonjin Lee

Keyword(s):

Galois Rings ◽

Dual Codes ◽

Characteristic P ◽

Lee Weights

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On cyclic codes over Galois rings

Discrete Applied Mathematics ◽

10.1016/j.dam.2018.01.017 ◽

2020 ◽

Vol 280 ◽

pp. 156-161 ◽

Cited By ~ 2

Author(s):

Jasbir Kaur ◽

Sucheta Dutt ◽

Ranjeet Sehmi

Keyword(s):

Cyclic Codes ◽

Galois Rings

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A Mass Formula and Rank of<tex>$BBZ_4$</tex>Cyclic Codes of Length<tex>$2^e$</tex>

IEEE Transactions on Information Theory ◽

10.1109/tit.2004.838109 ◽

2004 ◽

Vol 50 (12) ◽

pp. 3306-3312 ◽

Cited By ~ 16

Author(s):

T. Abualrub ◽

A. Ghrayeb ◽

R.H. Oehmke

Keyword(s):

Mass Formula ◽

Cyclic Codes

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Structures of high dimensional cyclic codes over Galois rings

Proceedings IEEE International Symposium on Information Theory, ◽

10.1109/isit.2002.1023445 ◽

2003 ◽

Author(s):

Peizhong Lu ◽

Mulan Liu

Keyword(s):

Cyclic Codes ◽

High Dimensional ◽

Galois Rings

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A transform approach to permutation groups of cyclic codes over Galois rings

IEEE Transactions on Information Theory ◽

10.1109/18.887849 ◽

2000 ◽

Vol 46 (7) ◽

pp. 2350-2358 ◽

Cited By ~ 11

Author(s):

D.K. Ray-Chaudhuri ◽

J.T. Blackford

Keyword(s):

Cyclic Codes ◽

Permutation Groups ◽

Galois Rings

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