Nonexistence of two classes of generalized bent functions
نویسندگان
چکیده
We obtain new nonexistence results of generalized bent functions from Z q to Zq (called type [n, q]) in the case that there exist cyclotomic integers in Z[ζq ] with absolute value q n 2 . This result generalize the previous two scattered nonexistence results [n, q] = [1, 2×7] of Pei [13] and [3, 2 × 23] of Jiang-Deng [7] to a generalized class. In the last section, we remark that this method can apply to the GBF from Z 2 to Zm.
منابع مشابه
New results on nonexistence of generalized bent functions
We get two kinds of new results on nonexistence of generalized bent function. The first one is Based on Feng’s results by using Schmidt’s field descent method. For the second kind, considering special property of the fieldQ(ζ23e), We get new nonexistence results of generalized bent functions with type [3, 2 · 23].
متن کاملThe Relationship between the Nonexistence of Generalized Bent Functions and Diophantine Equations
Two new results on the nonexistence of generalized bent functions are presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations, and examples satisfying our results are given.
متن کاملNonexistence of generalized bent functions and the quadratic norm form equations
We obtain the nonexistence of generalized bent functions (GBFs) from (\ZZ/t\ZZ)^n to \ZZ/t\ZZ (called type [n,t]), for a large new class. Specifically, by showing certain quadratic norm form equations have no integral points, we obtain the universal nonexistence of GBFs with type [n, 2p^e] for all sufficiently large p with respect to n and (p-1)/\ord_2(p), and by computational methods with a we...
متن کاملNonexistence of Generalized Bent Functions From $Z_{2}^{n}$ to $Z_{m}$
Several nonexistence results on generalized bent functions f : Zn 2 → Zm presented by using some knowledge on cyclotomic number fields and their imaginary quadratic subfields.
متن کاملAn Analysis of the 풞 Class of Bent Functions
Two (so-called C,D) classes of permutation-based bent Boolean functions were introduced by Carlet two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass D0). In this article, we look in more detail at the C class, and derive some existence and nonexistence results concerning the bent functions in the C class for many of the kno...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Des. Codes Cryptography
دوره 85 شماره
صفحات -
تاریخ انتشار 2017