Explicit Constructions of MDS Self-Dual Codes

Lin Sok

doi:10.1109/tit.2019.2954877

Explicit constructions of cyclic and negacyclic codes of length 3ps over 𝔽pm + u𝔽pm

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830920500639 ◽

2020 ◽

Vol 12 (05) ◽

pp. 2050063

Author(s):

Jirayu Phuto ◽

Chakkrid Klin-Eam

Keyword(s):

Algebraic Structures ◽

Dual Codes ◽

Chain Ring ◽

Negacyclic Codes ◽

Explicit Constructions ◽

Polynomial Formula

Let [Formula: see text] be a prime such that [Formula: see text]. The algebraic structures of all cyclic and negacyclic codes of length [Formula: see text] over the finite commutative chain ring [Formula: see text] are obtained that the conditions depend on the factorization of polynomial [Formula: see text] over [Formula: see text]. Therefore, we classify the structures of cyclic and negacyclic codes of length [Formula: see text] over [Formula: see text] into 2 cases, i.e., [Formula: see text] and [Formula: see text]. From that we obtain the number of all cyclic and negacyclic codes of length [Formula: see text] over [Formula: see text]. After that, we give some situations for such cyclic and negacyclic codes are self-dual codes.

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Construction of High-Rate Punctured Convolutional Codes through Dual Codes

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e98.a.1579 ◽

2015 ◽

Vol E98.A (7) ◽

pp. 1579-1583 ◽

Cited By ~ 1

Author(s):

Sen MORIYA ◽

Kana KIKUCHI ◽

Hiroshi SASANO

Keyword(s):

Convolutional Codes ◽

High Rate ◽

Dual Codes ◽

Punctured Convolutional Codes

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The Gender Troubles of Feofan Prokopovich

Canadian-American Slavic Studies ◽

10.30965/22102396-05401010 ◽

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.

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