scholarly journals Self-dual and complementary dual abelian codes over Galois rings

2019 ◽  
pp. 75-94
Author(s):  
Somphong Jitman ◽  
San Ling
Keyword(s):  
Galois Rings ◽  
Abelian Codes

scholarly journals Consta-Abelian Codes Over Galois Rings

2004 ◽  
Vol 50 (2) ◽  
pp. 367-380 ◽  
Author(s):  
Kiran. T ◽  
B.S. Rajan
Keyword(s):  
Galois Rings ◽  
Abelian Codes

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.

Semisimple cyclic and Abelian codes. II

Cybernetics ◽  
1970 ◽  
Vol 3 (3) ◽  
pp. 17-23 ◽  
Author(s):  
S. D. Berman
Keyword(s):  
Abelian Codes

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
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