Repeated Root Cyclic and Negacyclic Codes over Galois Rings

2009 ◽  
pp. 219-222 ◽  
Author(s):  
Sergio R. López-Permouth ◽  
Steve Szabo
Keyword(s):  
Galois Rings ◽  
Negacyclic Codes

Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings

2021 ◽  
Vol 28 (04) ◽  
pp. 581-600
Author(s):  
Hai Q. Dinh ◽  
Hualu Liu ◽  
Roengchai Tansuchat ◽  
Thang M. Vo
Keyword(s):  
Finite Field ◽  
Galois Ring ◽  
Maximum Distance ◽  
Galois Rings ◽  
Constacyclic Codes ◽  
Chain Ring ◽  
Negacyclic Codes ◽  
Singleton Bound ◽  
Maximum Distance Separable ◽  
Special Case

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].

scholarly journals On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings

2009 ◽  
Vol 3 (4) ◽  
pp. 409-420 ◽  
Author(s):  
Sergio R. López-Permouth ◽  
◽  
Steve Szabo
Keyword(s):  
Hamming Weight ◽  
Galois Rings ◽  
Negacyclic Codes

Negacyclic codes over Galois rings of characteristic 2 a

2011 ◽  
Vol 55 (4) ◽  
pp. 869-879 ◽  
Author(s):  
ShiXin Zhu ◽  
XiaoShan Kai
Keyword(s):  
Galois Rings ◽  
Negacyclic Codes ◽  
Characteristic 2

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

scholarly journals New Partial Difference Sets in Ztp2 and a Related Problem about Galois Rings

2001 ◽  
Vol 7 (1) ◽  
pp. 165-188 ◽  
Author(s):  
Xiang-Dong Hou ◽  
Ka Hin Leung ◽  
Qing Xiang
Keyword(s):  
Related Problem ◽  
Difference Sets ◽  
Galois Rings ◽  
Partial Difference ◽  
Partial Difference Sets

scholarly journals Construction of MDS self-dual codes over Galois rings

2007 ◽  
Vol 45 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Jon-Lark Kim ◽  
Yoonjin Lee
Keyword(s):  
Galois Rings ◽  
Dual Codes

scholarly journals Amorphous Association Schemes over the Galois Rings of Characteristic 4

1991 ◽  
Vol 12 (6) ◽  
pp. 513-526 ◽  
Author(s):  
Tatsuro Ito ◽  
Akihiro Munemasa ◽  
Mieko Yamada
Keyword(s):  
Association Schemes ◽  
Galois Rings

Quantum MDS and synchronizable codes from cyclic and negacyclic codes of length $$4p^s$$ over $${\mathbb {F}}_{p^m}$$

2021 ◽  
Vol 20 (11) ◽  
Author(s):  
Hai Q. Dinh ◽  
Ha T Le ◽  
Bac T. Nguyen ◽  
Roengchai Tansuchat
Keyword(s):  
Negacyclic Codes

On the minimum distance of negacyclic codes with two zeros

2019 ◽  
Vol 55 ◽  
pp. 134-150 ◽  
Author(s):  
Yajing Zhou ◽  
Xiaoshan Kai ◽  
Shixin Zhu ◽  
Jin Li
Keyword(s):  
Minimum Distance ◽  
Negacyclic Codes
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