Geodesic
Moments of codeword weights in random binary linear codes
Matematičeskie voprosy kriptografii, Tome 3 (2012), pp. 55-70.

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

We consider random uniform binary linear codes. Formulas for the first moments of weight spectrum are obtained along with the explicit estimates for the typical values of the minimal weight of nonzero codewords. Upper bounds for the probability of linear dependence between independent random binary vectors with given weights are obtained also. 
@article{MVK_2012_3_a2,
     author = {A. M. Zubkov and V. I. Kruglov},
     title = {Moments of codeword weights in random binary linear codes},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {55--70},
     publisher = {mathdoc},
     volume = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2012_3_a2/}
}
TY  - JOUR
AU  - A. M. Zubkov
AU  - V. I. Kruglov
TI  - Moments of codeword weights in random binary linear codes
JO  - Matematičeskie voprosy kriptografii
PY  - 2012
SP  - 55
EP  - 70
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2012_3_a2/
LA  - ru
ID  - MVK_2012_3_a2
ER  - 
%0 Journal Article
%A A. M. Zubkov
%A V. I. Kruglov
%T Moments of codeword weights in random binary linear codes
%J Matematičeskie voprosy kriptografii
%D 2012
%P 55-70
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2012_3_a2/
%G ru
%F MVK_2012_3_a2
A. M. Zubkov; V. I. Kruglov. Moments of codeword weights in random binary linear codes. Matematičeskie voprosy kriptografii, Tome 3 (2012), pp. 55-70. http://geodesic.mathdoc.fr/item/MVK_2012_3_a2/

[1] Abramovits M., Stigan I. (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979, 831 pp. | MR

[2] Alfers D., Dinges H., “A normal approximation for Beta and Gamma tail probabilities”, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 65 (1984), 399–420 | DOI | MR | Zbl

[3] Balakin G. V., “Raspredelenie ranga sluchainykh matrits nad konechnym polem”, Teoriya veroyatn. i primen., 13:4 (1968), 631–641 | MR | Zbl

[4] Balakin G. V., “Sistemy bulevykh uravnenii s iskazhennoi pravoi chastyu pri ogranicheniyakh na znacheniya neizvestnykh i oshibok”, Trudy po diskretnoi matematike, 11, no. 1, FIzmatlit, M., 2008, 5–17

[5] Zubkov A. M., Serov A. A., “Otsenki chisla bulevykh funktsii, imeyuschikh affinnye priblizheniya zadannoi tochnosti”, Diskretn. matem., 22:4 (2010), 3–19 | DOI | MR | Zbl

[6] Zubkov A. M., Serov A. A., “Polnoe dokazatelstvo universalnykh neravenstv dlya funktsii raspredeleniya binomialnogo zakona”, Teoriya veroyatn. i primen., 57:4 (2012) (to appear)

[7] Kozlov M. V., “O range matrits so sluchainymi bulevymi elementami”, DAN SSSR, 169:5 (1966), 1013–1016 | MR | Zbl

[8] Kovalenko I. N., “Ob odnoi predelnoi teoreme dlya opredelitelei v klasse bulevykh funktsii”, DAN SSSR, 161:3 (1964), 517–519 | MR

[9] Kopyttsev V. A., “O chisle reshenii sistem lineinykh bulevykh uravnenii v mnozhestve vektorov, obladayuschikh zadannym chislom edinits”, Diskretn. matem., 14:4 (2002), 87–109 | DOI | MR | Zbl

[10] Kopyttsev V. A., “O chisle reshenii sistemy sluchainykh lineinykh uravnenii v mnozhestve vektorov spetsialnogo vida”, Diskretn. matem., 18:1 (2006), 40–62 | DOI | MR | Zbl

[11] Kopyttsev V. A., Mikhailov V. G., “Teoremy puassonovskogo tipa dlya chisla spetsialnykh reshenii sluchainogo lineinogo vklyucheniya”, Diskretn. matem., 22:2 (2010), 3–21 | DOI | MR | Zbl

[12] Mikhailov V. G., “Predelnye teoremy dlya chisla tochek sluchainogo lineinogo podprostranstva, popavshikh v zadannoe mnozhestvo”, Diskretn. matem., 15:2 (2003), 128–137 | DOI | MR | Zbl

[13] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, M., 1982 | MR | Zbl

[14] Kholl M., Kombinatorika, Mir, M., 1970 | MR