Distribution of R-Patterns in the Highest Level of P-Adic Expansion of Some Linear Recursion Sequences Over Galois Rings

2003 ◽  
pp. 77-83 ◽  
Author(s):  
Zongduo Dai ◽  
Dingfeng Ye ◽  
Ping Wang ◽  
Genxi Fang
Keyword(s):  
Galois Rings ◽  
Linear Recursion

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 Ontology-Mediated Querying with the Description Logic EL: Trichotomy and Linear Datalog Rewritability

2017 ◽  
Author(s):  
Carsten Lutz ◽  
Leif Sabellek
Keyword(s):  
Description Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Data Complexity ◽  
First Order ◽  
Fine Grained ◽  
Linear Recursion

We consider ontology-mediated queries (OMQs) based on an EL ontology and an atomic query (AQ), provide an ultimately fine-grained analysis of data complexity and study rewritability into linear Datalog-aiming to capture linear recursion in SQL. Our main results are that every such OMQ is in AC0, NL-complete or PTime-complete, and that containment in NL coincides with rewritability into linear Datalog (whereas containment in AC0 coincides with rewritability into first-order logic). We establish natural characterizations of the three cases, show that deciding linear Datalog rewritability (as well as the mentioned complexities) is ExpTime-complete, give a way to construct linear Datalog rewritings when they exist, and prove that there is no constant bound on the arity of IDB relations in linear Datalog rewritings.

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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