scholarly journals On cyclotomic cosets and code constructions

2016 ◽  
Vol 488 ◽  
pp. 302-319 ◽  
Author(s):  
Giuliano G. La Guardia ◽  
Marcelo M.S. Alves
Keyword(s):  
Cyclotomic Cosets ◽  
Code Constructions

scholarly journals Subspace code constructions

2020 ◽  
Author(s):  
Antonio Cossidente ◽  
Giuseppe Marino ◽  
Francesco Pavese
Keyword(s):  
Code Constructions

Cyclotomy and arithmetic properties of some families in Z[x]/〈xpq − 1〉

2019 ◽  
Vol 13 (04) ◽  
pp. 2050077
Author(s):  
Sonal Jain ◽  
Sudhir Batra
Keyword(s):  
Finite Fields ◽  
Alternate Proof ◽  
Generalized Cyclotomy ◽  
Cyclotomic Cosets ◽  
Arithmetic Properties

Cyclotomic classes of order 2 with respect to a product of two distinct odd primes [Formula: see text] and [Formula: see text] are represented in some specific forms and using these forms an alternate proof of Theorem 3 of [C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl. 4 (1998) 140–166] is given, when [Formula: see text]. Further, it is observed that these classes are related to [Formula: see text]-cyclotomic cosets, where [Formula: see text] and [Formula: see text] such that gcd([Formula: see text]. Finally, arithmetic properties of some families in [Formula: see text] and hence in [Formula: see text] are studied.

scholarly journals Z6-Code Constructions of the Leech Lattice and the Niemeier Lattices

2002 ◽  
Vol 23 (5) ◽  
pp. 573-581 ◽  
Author(s):  
Masaaki Harada ◽  
Masaaki Kitazume
Keyword(s):  
Leech Lattice ◽  
Code Constructions

scholarly journals A Survey of Linear Network Coding and Network Error Correction Code Constructions and Algorithms

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Michele Sanna ◽  
Ebroul Izquierdo
Keyword(s):  
Network Coding ◽  
Network Control ◽  
Practical Implementation ◽  
Error Protection ◽  
New Paradigm ◽  
Linear Network ◽  
Linear Network Coding ◽  
Store And Forward ◽  
Code Constructions ◽  
Construction Algorithms

Network coding was introduced by Ahlswede et al. in a pioneering work in 2000. This paradigm encompasses coding and retransmission of messages at the intermediate nodes of the network. In contrast with traditional store-and-forward networking, network coding increases the throughput and the robustness of the transmission. Linear network coding is a practical implementation of this new paradigm covered by several research works that include rate characterization, error-protection coding, and construction of codes. Especially determining the coding characteristics has its importance in providing the premise for an efficient transmission. In this paper, we review the recent breakthroughs in linear network coding for acyclic networks with a survey of code constructions literature. Deterministic construction algorithms and randomized procedures are presented for traditional network coding and for network-control network coding.

scholarly journals Code Constructions for Distributed Storage With Low Repair Bandwidth and Low Repair Complexity

2018 ◽  
Vol 66 (12) ◽  
pp. 5847-5860 ◽  
Author(s):  
Siddhartha Kumar ◽  
Alexandre Graell i Amat ◽  
Iryna Andriyanova ◽  
Fredrik Brannstrom ◽  
Eirik Rosnes
Keyword(s):  
Distributed Storage ◽  
Code Constructions
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