Basic Notions on Codes Over Galois Rings

2002 ◽  
pp. 145-165
Author(s):  
Gilberto Bini ◽  
Flaminio Flamini
Keyword(s):  
Galois Rings

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

scholarly journals An Upper Bound for the Extended Kloosterman Sums over Galois Rings

1998 ◽  
Vol 4 (3) ◽  
pp. 218-238 ◽  
Author(s):  
Abhijit G. Shanbhag ◽  
P. Vijay Kumar ◽  
Tor Helleseth
Keyword(s):  
Upper Bound ◽  
Kloosterman Sums ◽  
Galois Rings
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