Constructions of specific permutation codes for multi-user communication

2002 ◽  
Author(s):  
V.B. Balakirsky ◽  
A.J. Han Vinck
Keyword(s):  
Permutation Codes

scholarly journals A Bound on Permutation Codes

10.37236/2929 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Jürgen Bierbrauer ◽  
Klaus Metsch
Keyword(s):  
Projective Plane ◽  
Symmetric Group ◽  
Minimum Distance ◽  
Main Part ◽  
Latin Squares ◽  
Permutation Codes ◽  
Permutation Code ◽  
Mutually Orthogonal Latin Squares ◽  
Hamming Metric ◽  
Completion Theorem

Consider the symmetric group $S_n$ with the Hamming metric. A  permutation code on $n$ symbols is a subset $C\subseteq S_n.$ If $C$ has minimum distance $\geq n-1,$ then $\vert C\vert\leq n^2-n.$ Equality can be reached if and only if a projective plane of order $n$ exists. Call $C$ embeddable if it is contained in a permutation code of minimum distance $n-1$ and cardinality $n^2-n.$ Let $\delta =\delta (C)=n^2-n-\vert C\vert$ be the deficiency of the permutation code $C\subseteq S_n$ of minimum distance $\geq n-1.$We prove that $C$ is embeddable if either $\delta\leq 2$ or if $(\delta^2-1)(\delta +1)^2<27(n+2)/16.$ The main part of the proof is an adaptation of the method used to obtain the famous Bruck completion theorem for mutually orthogonal latin squares.

A note on good permutation codes from Reed–Solomon codes

2019 ◽  
Vol 87 (10) ◽  
pp. 2335-2340
Author(s):  
R. Sobhani ◽  
A. Abdollahi ◽  
J. Bagherian ◽  
M. Khatami
Keyword(s):  
Permutation Codes ◽  
Reed Solomon Codes

Coset Partitioning Construction of Systematic Permutation Codes Under the Chebyshev Metric

2019 ◽  
Vol 67 (6) ◽  
pp. 3842-3851
Author(s):  
Hui Han ◽  
Jianjun Mu ◽  
Yu-Cheng He ◽  
Xiaopeng Jiao
Keyword(s):  
Permutation Codes

Path-Permutation Codes for End-to-End Transmission in Ad Hoc Cognitive Radio Networks

2015 ◽  
Vol 14 (6) ◽  
pp. 3309-3321 ◽  
Author(s):  
I-Wei Lai ◽  
Chia-Han Lee ◽  
Kwang-Cheng Chen ◽  
Ezio Biglieri
Keyword(s):  
Cognitive Radio ◽  
Cognitive Radio Networks ◽  
Ad Hoc ◽  
Radio Networks ◽  
Permutation Codes ◽  
End To End

Constructions for Permutation Codes in Powerline Communications

2004 ◽  
Vol 32 (1-3) ◽  
pp. 51-64 ◽  
Author(s):  
Wensong Chu ◽  
Charles J. Colbourn ◽  
Peter Dukes
Keyword(s):  
Permutation Codes ◽  
Powerline Communications
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