scholarly journals Small weight codewords in the LDPC codes arising from linear representations of geometries

2009 ◽  
Vol 17 (1) ◽  
pp. 1-24 ◽  
Author(s):  
V. Pepe ◽  
L. Storme ◽  
G. Van de Voorde
Keyword(s):  
Ldpc Codes ◽  
Small Weight ◽  
Linear Representations ◽  
Small Weight Codewords

Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles

2006 ◽  
Vol 42 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Jon-Lark Kim ◽  
Keith E. Mellinger ◽  
Leo Storme
Keyword(s):  
Ldpc Codes ◽  
Generalized Quadrangles ◽  
Small Weight ◽  
Small Weight Codewords

scholarly journals LDPC codes associated with linear representations of geometries

2010 ◽  
Vol 4 (3) ◽  
pp. 405-417 ◽  
Author(s):  
Peter Vandendriessche ◽  
Keyword(s):  
Ldpc Codes ◽  
Linear Representations

scholarly journals Minimal codewords arising from the incidence of points and hyperplanes in projective spaces

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Daniele Bartoli ◽  
Lins Denaux
Keyword(s):  
Projective Space ◽  
Linear Combination ◽  
Projective Spaces ◽  
Sufficient Condition ◽  
Small Weight ◽  
The Past ◽  
Small Weight Codewords

<p style='text-indent:20px;'>Over the past few years, the codes <inline-formula><tex-math id="M1">\begin{document}$ {\mathcal{C}}_{n-1}(n,q) $\end{document}</tex-math></inline-formula> arising from the incidence of points and hyperplanes in the projective space <inline-formula><tex-math id="M2">\begin{document}$ {\rm{PG}}(n,q) $\end{document}</tex-math></inline-formula> attracted a lot of attention. In particular, small weight codewords of <inline-formula><tex-math id="M3">\begin{document}$ {\mathcal{C}}_{n-1}(n,q) $\end{document}</tex-math></inline-formula> are a topic of investigation. The main result of this work states that, if <inline-formula><tex-math id="M4">\begin{document}$ q $\end{document}</tex-math></inline-formula> is large enough and not prime, a codeword having weight smaller than roughly <inline-formula><tex-math id="M5">\begin{document}$ \frac{1}{2^{n-2}}q^{n-1}\sqrt{q} $\end{document}</tex-math></inline-formula> can be written as a linear combination of a few hyperplanes. Consequently, we use this result to provide a graph-theoretical sufficient condition for these codewords of small weight to be minimal.</p>

scholarly journals On the small-weight codewords of some Hermitian codes

2016 ◽  
Vol 73 ◽  
pp. 27-45 ◽  
Author(s):  
Chiara Marcolla ◽  
Marco Pellegrini ◽  
Massimiliano Sala
Keyword(s):  
Small Weight ◽  
Hermitian Codes ◽  
Small Weight Codewords

scholarly journals An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n,q)

2009 ◽  
Vol 116 (4) ◽  
pp. 996-1001 ◽  
Author(s):  
Michel Lavrauw ◽  
Leo Storme ◽  
Peter Sziklai ◽  
Geertrui Van de Voorde
Keyword(s):  
Empty Interval ◽  
Small Weight ◽  
Small Weight Codewords

MET-LDPC Code Ensembles of Low Code Rates with Exponentially Few Small Weight Codewords

2021 ◽  
pp. 1-1
Author(s):  
Suhwang Jeong ◽  
Jeongseok Ha
Keyword(s):  
Ldpc Code ◽  
Small Weight ◽  
Small Weight Codewords

scholarly journals Linear representations of finite geometries and associated LDPC codes

2020 ◽  
Vol 173 ◽  
pp. 105238
Author(s):  
Peter Sin ◽  
Julien Sorci ◽  
Qing Xiang
Keyword(s):  
Ldpc Codes ◽  
Finite Geometries ◽  
Linear Representations

scholarly journals Stability of k mod p multisets and small weight codewords of the code generated by the lines of PG(2,q)

2018 ◽  
Vol 157 ◽  
pp. 321-333 ◽  
Author(s):  
Tamás Szőnyi ◽  
Zsuzsa Weiner
Keyword(s):  
Small Weight ◽  
Small Weight Codewords ◽  
Mod P

scholarly journals A study of intersections of quadrics having applications on the small weight codewords of the functional codes C2(Q), Q a non-singular quadric

2010 ◽  
Vol 214 (10) ◽  
pp. 1729-1739 ◽  
Author(s):  
F.A.B. Edoukou ◽  
A. Hallez ◽  
F. Rodier ◽  
L. Storme
Keyword(s):  
Small Weight ◽  
Small Weight Codewords ◽  
Functional Codes ◽  
Singular Quadric
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