Subset sums over Galois rings

2019 ◽  
Vol 205 ◽  
pp. 148-169
Author(s):  
Yuchen Ding ◽  
Haiyan Zhou
Keyword(s):  
Galois Rings ◽  
Subset Sums

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 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 Counting polynomial subset sums

2018 ◽  
Vol 47 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Jiyou Li ◽  
Daqing Wan
Keyword(s):  
Subset Sums ◽  
Counting Polynomial

scholarly journals On representation of r-th powers by subset sums

1989 ◽  
Vol 52 (4) ◽  
pp. 353-365 ◽  
Author(s):  
E. Lipkin
Keyword(s):  
Subset Sums

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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