Self-dual codes from circulant matrices

2011 ◽  
Vol 64 (1-2) ◽  
pp. 129-141 ◽  
Author(s):  
S. D. Georgiou ◽  
E. Lappas
2021 ◽  
Vol 344 (11) ◽  
pp. 112590
Author(s):  
J. Gildea ◽  
A. Kaya ◽  
R. Taylor ◽  
A. Tylyshchak ◽  
B. Yildiz

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Joe Gildea ◽  
Abidin Kaya ◽  
Adam Michael Roberts ◽  
Rhian Taylor ◽  
Alexander Tylyshchak

<p style='text-indent:20px;'>In this paper, we construct new self-dual codes from a construction that involves a unique combination; <inline-formula><tex-math id="M1">\begin{document}$ 2 \times 2 $\end{document}</tex-math></inline-formula> block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{F}_2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_2+u \mathbb{F}_2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{F}_4+u \mathbb{F}_4 $\end{document}</tex-math></inline-formula>. Using extensions and neighbours of codes, we construct <inline-formula><tex-math id="M5">\begin{document}$ 32 $\end{document}</tex-math></inline-formula> new self-dual codes of length <inline-formula><tex-math id="M6">\begin{document}$ 68 $\end{document}</tex-math></inline-formula>. We construct 48 new best known singly-even self-dual codes of length 96.</p>


2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Joe Gildea ◽  
◽  
Adrian Korban ◽  
Abidin Kaya ◽  
Bahattin Yildiz ◽  
...  

2020 ◽  
Vol 54 (1-3) ◽  
pp. 198-228
Author(s):  
Gary Marker

Abstract This essay constitutes a close reading of the works of Feofan Prokopovich that touch upon gender and womanhood. Interpretively it is informed by Judith Butler’s book Gender Trouble, specifically by her model of gender-as-performance. Prokopovich’s writings conveyed a negative characterization of holy women and Russian women of power, a combination of glaring silences and Scholastic dual codes that in toto denied the association of womanhood with glory or wisdom. In this he stood apart from other East Slavic Orthodox homilists of his day, even though they too invariably associated virtue with masculinity (muzhestvo). For Prokopovich, wisdom, strength, constancy, etc., were innately masculine. Women, by contrast, were weak, inconstant, non-rational, and guided by emotion. His sermons nominally in praise of Catherine I and Anna Ioannovna were suffused with narrative gestures that, to those attuned to the nuances of Scholastic rhetoric, ran entirely counter to their nominal message. Several panegyrics to Anna, for example, made no mention of her at all, a practice in sharp contrast to his sermons to male rulers, which typically placed the honoree firmly in the foreground. Even more startling is his singularly minimalist approach to Mary, for whom he composed almost no sermons and whose presence he barely mentioned in tracts where one would have expected otherwise. This essay concludes that this attitude reflected both his personal preferences and influence that Protestant Pietism had on his thinking.


2019 ◽  
Vol 14 (2) ◽  
pp. 443-456
Author(s):  
Simon Eisenbarth ◽  
Gabriele Nebe
Keyword(s):  

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