RUS  ENG
Full version
JOURNALS // Problemy Peredachi Informatsii

Probl. Peredachi Inf., 2008, Volume 44, Issue 1, Pages 15–37 (Mi ppi1263)

Bent and Hyper-bent Functions over a Field of $2^l$ Elements
A. S. Kuz'min, V. T. Markov, A. A. Nechaev, V. A. Shishkin, A. B. Shishkov

References

1. Youssef A. M., Gong G., “Hyper–Bent Functions”, Advances in Cryptology, Proc. of Eurocrypt' 2001, Lecture Notes in Computer Science, 2045, Springer-Verlag, Berlin, 2001, 406–419  mathscinet  zmath
2. Solodovnikov V. I., “Bent-funktsii iz konechnoi abelevoi gruppy v konechnuyu abelevu gruppu”, Diskretnaya matematika, 14:1 (2002), 99–113  mathnet  mathscinet  zmath
3. Dillon J. F., “A Survey of Bent Functions”, NSA Techn. J., Special Issue (1972), 191–215
4. Rothaus O. S., “On “Bent” Functions”, J. Combin. Theory Ser. A, 20:3 (1976), 300–305  crossref  mathscinet  zmath
5. Kuzmin A. S., Markov V. T., Nechaev A. A., Shishkov A. B., “Priblizhenie bulevykh funktsii monomialnymi”, Diskretnaya matematika, 18:1 (2006), 9–29  mathnet  mathscinet  zmath
6. Dillon J. F., Elementary Hadamard Difference Sets, Ph. D. Dissertation, Univ. Maryland, Maryland, 1974  mathscinet
7. Carlet C., “Two New Classes of Bent Functions”, Advances in Cryptology, Proc. of Eurocrypt' 1993, Lecture Notes in Computer Science, 765, Springer-Verlag, Berlin, 1994, 77–101  mathscinet  zmath
8. Carlet C., “Generalized Partial Spreads”, IEEE Trans. Inform. Theory, 41:5 (1995), 1482–1487  crossref  mathscinet  zmath
9. Carlet C., “A Construction of Bent Functions”, Proc. Seventh Joint Swedish–Russian Int. Workshop on Information Theory (St.-Petersburg, Russia. June 17–22, 1995), 57–59  mathscinet
10. Kumar P. V., Sholtz R. A., Welch L. R., “Generalized Bent Functions and Their Properties”, J. Combin. Theory Ser. A, 40:1 (1985), 90–107  crossref  mathscinet  zmath
11. Chung H., Kumar P. V., “A New General Construction for Generalized Bent Functions”, IEEE Trans. Inform. Theory, 35:1 (1989), 206–209  crossref  mathscinet  zmath
12. Nyberg K., “Construction of Bent Functions and Difference Sets”, Proc. of Eurocrypt'1990, Lecture Notes in Computer Science, 473, Springer-Verlag, Berlin, 1991, 151–160  mathscinet
13. Ambrosimov A. S., “Svoistva bent-funktsii $q$-znachnoi logiki nad konechnymi polyami”, Diskretnaya matematika, 6:3 (1994), 50–60  mathnet  mathscinet  zmath
14. Logachev O. A., Salnikov A. A., Yaschenko V. V., “Bent-funktsii na konechnoi abelevoi gruppe”, Diskretnaya matematika, 9:4 (1997), 3–20  mathnet  mathscinet  zmath
15. Carlet C., “Hyper-bent Functions”, Proc. PRAGOCRYPT'96, Czech Techn. Univ. Publ., Prague, 1996, 145–155  mathscinet
16. Carlet C., Gaborit Ph., “Hyper-bent Functions and Cyclic Codes”, J. Combin. Theory Ser. A, 113:3 (2006), 466–482  crossref  mathscinet  zmath
17. Kuzmin A. S., Nechaev A. A., Shishkin V. A., “Bent- i giper-bent-funktsii nad polem iz $2^l$ elementov”, Trudy po diskretnoi matematike, 10, Gelios ARV, M., 2007, 86–111
18. The Cunningham Project, http://homes.cerias.purdue.edu/~ssw/cun/index.html
19. Lidl R., Niderraiter G., Konechnye polya, T. 1, 2, Mir, M., 1988  zmath
20. Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Ch. 2, Gelios ARV, M., 2003
21. Mak-Vilyams F. Dzh., Sloen N. Dzh., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979


© Steklov Math. Inst. of RAS, 2026