Solving undetermined systems of linear Boolean equations with corrupted right-hand side and low-weight true solution
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 235-237.

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

Undetermined systems of random linear Boolean equations with corrupted right-hand side and with a true solution of little Hamming weight are studied. Experimentally, we show that, for small bit-error rates, these systems can be efficiently solved by decoding algorithms with regard to information symbols.
Keywords: random systems of linear Boolean equations, information-set decoding.
@article{PDMA_2019_12_a63,
     author = {N. Yu. Rumenko and A. V. Kostyuk},
     title = {Solving undetermined systems of linear {Boolean} equations with corrupted right-hand side and low-weight true solution},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {235--237},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a63/}
}
TY  - JOUR
AU  - N. Yu. Rumenko
AU  - A. V. Kostyuk
TI  - Solving undetermined systems of linear Boolean equations with corrupted right-hand side and low-weight true solution
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2019
SP  - 235
EP  - 237
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2019_12_a63/
LA  - ru
ID  - PDMA_2019_12_a63
ER  - 
%0 Journal Article
%A N. Yu. Rumenko
%A A. V. Kostyuk
%T Solving undetermined systems of linear Boolean equations with corrupted right-hand side and low-weight true solution
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2019
%P 235-237
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2019_12_a63/
%G ru
%F PDMA_2019_12_a63
N. Yu. Rumenko; A. V. Kostyuk. Solving undetermined systems of linear Boolean equations with corrupted right-hand side and low-weight true solution. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 235-237. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a63/

[1] Balakin G. V., “Vvedenie v teoriyu sluchainykh sistem uravnenii”, Trudy po diskretnoi matematike, v. 1, TVP, M., 1997, 1–18 | MR

[2] Alekseichuk A. N., Gryaznukhin A. Yu., “Bystryi algoritm vosstanovleniya istinnogo resheniya fiksirovannogo vesa sistemy lineinykh bulevykh uravnenii s iskazhennoi pravoi chastyu”, Prikladnaya diskretnaya matematika, 20:2 (2013), 59–70 | MR

[3] Varshamov R. R., “Otsenka chisla signalov v kodakh s korrektsiei oshibok”, Doklady AN SSSR, 1957, 739–741 | Zbl

[4] May A., Meurer A., Thomae E., “Decoding random linear codes in O$(2^{0.054n})$”, Proc. Asiacrypt'2011 (Seoul, South Korea, December 04–08, 2011), 107–124 | MR