Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉

2022 ◽  
Vol 78 ◽  
pp. 101972
Author(s):  
Boran Kim ◽  
Nayoung Han ◽  
Yoonjin Lee
Keyword(s):  
Chain Ring ◽  
Orthogonal Codes

Quantum codes from cyclic codes over F3 + vF3

2014 ◽  
Vol 12 (06) ◽  
pp. 1450042 ◽  
Author(s):  
Mohammad Ashraf ◽  
Ghulam Mohammad
Keyword(s):  
Commutative Ring ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Quantum Codes ◽  
Quantum Code ◽  
Chain Ring ◽  
Arbitrary Length ◽  
Orthogonal Codes ◽  
Finite Commutative Ring ◽  
A Chain

Let R = F3 + vF3 be a finite commutative ring, where v2 = 1. It is a finite semi-local ring, not a chain ring. In this paper, we give a construction for quantum codes from cyclic codes over R. We derive self-orthogonal codes over F3 as Gray images of linear and cyclic codes over R. In particular, we use two codes associated with a cyclic code over R of arbitrary length to determine the parameters of the corresponding quantum code.

Cyclic self-orthogonal codes over finite chain ring

2018 ◽  
Vol 11 (06) ◽  
pp. 1850078 ◽  
Author(s):  
Abhay Kumar Singh ◽  
Narendra Kumar ◽  
Kar Ping Shum
Keyword(s):  
Prime Number ◽  
Cyclic Codes ◽  
Sufficient Condition ◽  
Galois Rings ◽  
Finite Chain ◽  
Necessary And Sufficient Condition ◽  
Chain Ring ◽  
Finite Chain Ring ◽  
Orthogonal Codes ◽  
Necessary And Sufficient

In this paper, we study the cyclic self-orthogonal codes over a finite commutative chain ring [Formula: see text], where [Formula: see text] is a prime number. A generating polynomial of cyclic self-orthogonal codes over [Formula: see text] is obtained. We also provide a necessary and sufficient condition for the existence of nontrivial self-orthogonal codes over [Formula: see text]. Finally, we determine the number of the above codes with length [Formula: see text] over [Formula: see text] for any [Formula: see text]. The results are given by Zhe-Xian Wan on cyclic codes over Galois rings in [Z. Wan, Cyclic codes over Galois rings, Algebra Colloq. 6 (1999) 291–304] are extended and strengthened to cyclic self-orthogonal codes over [Formula: see text].

Orthogonal codes-based dynamic spectrum access in cognitive radio networks

2019 ◽  
Vol 16 (12) ◽  
pp. 34-46
Author(s):  
Ehab F. Badran ◽  
Amr A. Bashir ◽  
Amira I. Zaki ◽  
Waleed K. Badawi
Keyword(s):  
Cognitive Radio ◽  
Cognitive Radio Networks ◽  
Dynamic Spectrum Access ◽  
Radio Networks ◽  
Dynamic Spectrum ◽  
Spectrum Access ◽  
Orthogonal Codes

Large Families of Asymptotically Optimal Two-Dimensional Optical Orthogonal Codes

2012 ◽  
Vol 58 (2) ◽  
pp. 1163-1185 ◽  
Author(s):  
Reza Omrani ◽  
Gagan Garg ◽  
P. Vijay Kumar ◽  
Petros Elia ◽  
Pankaj Bhambhani
Keyword(s):  
Two Dimensional ◽  
Asymptotically Optimal ◽  
Optical Orthogonal Codes ◽  
Orthogonal Codes ◽  
Large Families
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