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) no. 4, pp. 101-124 
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) no. 4, pp. 101-124. http://geodesic.mathdoc.fr/item/MVK_2018_9_4_a5/
@article{MVK_2018_9_4_a5,
     author = {V. N. Sachkov and I. A. Kruglov},
     title = {Moments of the weight deficit of a random equiprobable involution acting on a vector space over a field of two elements},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {101--124},
     year = {2018},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2018_9_4_a5/}
}
TY  - JOUR
AU  - V. N. Sachkov
AU  - I. A. Kruglov
TI  - Moments of the weight deficit of a random equiprobable involution acting on a vector space over a field of two elements
JO  - Matematičeskie voprosy kriptografii
PY  - 2018
SP  - 101
EP  - 124
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MVK_2018_9_4_a5/
LA  - ru
ID  - MVK_2018_9_4_a5
ER  - 
%0 Journal Article
%A V. N. Sachkov
%A I. A. Kruglov
%T Moments of the weight deficit of a random equiprobable involution acting on a vector space over a field of two elements
%J Matematičeskie voprosy kriptografii
%D 2018
%P 101-124
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/MVK_2018_9_4_a5/
%G ru
%F MVK_2018_9_4_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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.