scholarly journals Codes over a family of local Frobenius rings, Gray maps and self-dual codes

2017 ◽  
Vol 217 ◽  
pp. 512-524 ◽  
Author(s):  
Steven T. Dougherty ◽  
Esengül Saltürk
Keyword(s):  
Dual Codes ◽  
Frobenius Rings ◽  
Gray Maps

scholarly journals Self-dual codes over commutative Frobenius rings

2010 ◽  
Vol 16 (1) ◽  
pp. 14-26 ◽  
Author(s):  
Steven T. Dougherty ◽  
Jon-Lark Kim ◽  
Hamid Kulosman ◽  
Hongwei Liu
Keyword(s):  
Dual Codes ◽  
Frobenius Rings

scholarly journals Double bordered constructions of self-dual codes from group rings over Frobenius rings

2020 ◽  
Vol 12 (4) ◽  
pp. 769-784
Author(s):  
Joe Gildea ◽  
Rhian Taylor ◽  
Abidin Kaya ◽  
A. Tylyshchak
Keyword(s):  
Group Rings ◽  
Dual Codes ◽  
Weight Enumerators ◽  
Frobenius Rings ◽  
Construction Of Self ◽  
New Construction ◽  
New Codes

AbstractIn this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings $\mathbb {F}_{2}+u\mathbb {F}_{2}$ F 2 + u F 2 and $\mathbb {F}_{4}+u\mathbb {F}_{4}$ F 4 + u F 4 . We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables.

scholarly journals New binary self-dual codes of lengths 80, 84 and 96 from composite matrices

2021 ◽  
Author(s):  
Joe Gildea ◽  
Adrian Korban ◽  
Adam Michael Roberts
Keyword(s):  
Group Rings ◽  
Dual Codes ◽  
Frobenius Rings

AbstractIn this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative Frobenius rings. By applying these techniques over different alphabets, we construct best known singly-even binary self-dual codes of lengths 80, 84 and 96 as well as doubly-even binary self-dual codes of length 96 that were not known in the literature before.

The Gender Troubles of Feofan Prokopovich

2020 ◽  
Vol 54 (1-3) ◽  
pp. 198-228
Author(s):  
Gary Marker
Keyword(s):  
Sharp Contrast ◽  
Close Reading ◽  
Dual Codes ◽  
Minimalist Approach ◽  
Holy Women ◽  
Gender Trouble

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.

A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2237-2248 ◽  
Author(s):  
Habibul Islam ◽  
Om Prakash
Keyword(s):  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Gray Maps ◽  
Permutation Equivalent ◽  
Quasi Cyclic Codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

Self-Dual Codes Over Chain Rings

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