scholarly journals Self-orthogonal codes over a non-unital ring and combinatorial matrices

2021 ◽  
Author(s):  
Minjia Shi ◽  
Shukai Wang ◽  
Jon-Lark Kim ◽  
Patrick Solé
Keyword(s):  
Unital Ring ◽  
Orthogonal Codes

scholarly journals The build-up construction of quasi self-dual codes over a non-unital ring

2021 ◽  
pp. 2250143
Author(s):  
Adel Alahmadi ◽  
Alaa Altassan ◽  
Hatoon Shoaib ◽  
Amani Alkathiry ◽  
Alexis Bonnecaze ◽  
...  
Keyword(s):  
Local Ring ◽  
Recursive Construction ◽  
Dual Codes ◽  
Generators And Relations ◽  
Unital Ring ◽  
Type Iv ◽  
Orthogonal Codes ◽  
Construction Of Self

There is a local ring [Formula: see text] of order [Formula: see text] without identity for the multiplication, defined by generators and relations as [Formula: see text] We study a recursive construction of self-orthogonal codes over [Formula: see text] We classify, up to permutation equivalence, self-orthogonal codes of length [Formula: see text] and size [Formula: see text] (called here quasi self-dual codes or QSD) up to the length [Formula: see text]. In particular, we classify Type IV codes (QSD codes with even weights) up to [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

scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

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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