Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 4, pp. 101-124
Citer cet article
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
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.
