Multi-Erasure Locally Recoverable Codes Over Small Fields: A Tensor Product Approach

2020 ◽  
Vol 66 (5) ◽  
pp. 2609-2624 ◽  
Author(s):  
Pengfei Huang ◽  
Eitan Yaakobi ◽  
Paul H. Siegel
Keyword(s):  
Tensor Product ◽  
Small Fields ◽  
Product Approach ◽  
Locally Recoverable Codes

Semi-tensor product approach to networked evolutionary games

2014 ◽  
Vol 12 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Daizhan Cheng ◽  
Hongsheng Qi ◽  
Fehuang He ◽  
Tingting Xu ◽  
Hairong Dong
Keyword(s):  
Tensor Product ◽  
Evolutionary Games ◽  
Product Approach

Finding Cut-Edges and the Minimum Spanning Tree via Semi-Tensor Product Approach

2018 ◽  
Vol 6 (5) ◽  
pp. 459-472
Author(s):  
Xujiao Fan ◽  
Yong Xu ◽  
Xue Su ◽  
Jinhuan Wang
Keyword(s):  
Tensor Product ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Product Approach ◽  
Matrix Expression ◽  
Necessary And Sufficient ◽  
Logical Functions

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.

scholarly journals Perfect hypercomplex algebras: Semi-tensor product approach

2021 ◽  
Vol 1 (4) ◽  
pp. 177-187
Author(s):  
Daizhan Cheng ◽  
◽  
Zhengping Ji ◽  
Jun-e Feng ◽  
Shihua Fu ◽  
...  
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Characteristic Functions ◽  
Hypercomplex Numbers ◽  
3 Dimensional ◽  
Zero Sets ◽  
Higher Dimensional ◽  
Product Approach ◽  
Necessary And Sufficient

<abstract><p>The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product (STP) of matrices are reviewed. The zero sets are defined for non-invertible hypercomplex numbers in a given PHA, and characteristic functions are proposed for calculating zero sets. Then PHA of various dimensions are considered. First, classification of $ 2 $-dimensional PHAs are investigated. Second, all the $ 3 $-dimensional PHAs are obtained and the corresponding zero sets are calculated. Finally, $ 4 $- and higher dimensional PHAs are also considered.</p></abstract>

scholarly journals Tensor Product Approach to Quantum Control

2019 ◽  
pp. 367-379
Author(s):  
Diego Quiñones-Valles ◽  
Sergey Dolgov ◽  
Dmitry Savostyanov
Keyword(s):  
Tensor Product ◽  
Quantum Control ◽  
Product Approach
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