Geodesic
Moments of the weight deficit of a random equiprobable involution acting on a vector space over a field of two elements
Matematičeskie voprosy kriptografii, Tome 9 (2018), pp. 101-124.

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For the additive group of a vector space of increasing dimension $m$ over a field of two elements we study the moments of a random variable equal to the weight deficit of a random equiprobable involution formed by the product of $2^{m-1}$ independent binary cycles. Exact and asymptotic formulas for the binomial moments and for the variance are obtained. 
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V. N. Sachkov; I. A. Kruglov. Moments of the weight deficit of a random equiprobable involution acting on a vector space over a field of two elements. Matematičeskie voprosy kriptografii, Tome 9 (2018), pp. 101-124. http://geodesic.mathdoc.fr/item/MVK_2018_9_a5/

[1] Sachkov V. N., “Kombinatornye svoistva differentsialno 2-ravnomernykh podstanovok”, Matematicheskie voprosy kriptografii, 6:1 (2015), 159–179 | DOI

[2] Sachkov V. N., Kruglov I. A., “Vesovye defitsity involyutsii i podstanovok”, Matematicheskie voprosy kriptografii, 7:4 (2016), 95–116 | DOI

[3] Sachkov V. N., “Involyutsii s dannym vesovym defitsitom, sootvetstvuyuschie tablitse Keli konechnoi abelevoi gruppy”, Matematicheskie voprosy kriptografii, 8:4 (2017), 117–134 | DOI

[4] Sachkov V. N., Kurs kombinatornogo analiza, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2013, 336 pp.