Related papers: Nonexistence of certain classes of generalized ben…
We obtain new non-existence results of generalized bent functions from \ZZ^n_q to \ZZ_q (called type [n,q]). The first case is a class of types where q=2p_1^{r_1}p_2^{r_2}. The second case contains two types [1 <= n <= 3, 2 * 31^e]$ and [1…
We obtain new nonexistence results of generalized bent functions from $\{Z^n}_q$ to $\Z_q$ (called type $[n,q]$) in the case that there exist cyclotomic integers in $ \Z[\zeta_{q}]$ with absolute value $q^{\frac{n}{2}}$. This result…
We present a new result on the nonexistence of generalized bent functions (GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no…
In this paper, we present some new nonexistence results on $(m,n)$-generalized bent functions, which improved recent results. More precisely, we derive new nonexistence results for general $n$ and $m$ odd or $m \equiv 2 \pmod{4}$, and…
In this paper, we investigate generalized bent functions (GBFs) from $\mathbb{Z}_3^n$ to $\mathbb{Z}_m$. We show that GBFs exist whenever $3$ divides $m$, while several nonexistence results are obtained when $3\nmid m$. In particular, we…
Generalized bent (gbent) functions is a class of functions $f: \mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$, where $q \geq 2$ is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot…
In this paper, we investigate properties of functions from $\mathbb{Z}_{p}^n$ to $\mathbb{Z}_q$, where $p$ is an odd prime and $q$ is a positive integer divided by $p$. we present the sufficient and necessary conditions for bent-ness of…
Several nonexistence results on generalized bent functions $f:Z_{2}^{n} \rightarrow Z_{m}$ presented by using some knowledge on cyclotomic number fields and their imaginary quadratic subfields.
In difference to many recent articles that deal with generalized bent (gbent) functions $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$ for certain small valued $q\in \{4,8,16 \}$, we give a complete description of these functions for both $n$…
Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over…
In this paper, we study the dual of generalized bent functions $f: V_{n}\rightarrow \mathbb{Z}_{p^k}$ where $V_{n}$ is an $n$-dimensional vector space over $\mathbb{F}_{p}$ and $p$ is an odd prime, $k$ is a positive integer. It is known…
Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine…
We prove new non-existence results for vectorial monomial Dillon type bent functions mapping the field of order $2^{2m}$ to the field of order $2^{m/3}$. When $m$ is odd and $m>3$ we show that there are no such functions. When $m$ is even…
Negabent functions were introduced as a generalization of bent functions, which have applications in coding theory and cryptography. In this paper, we have extended the notion of negabent functions to the functions defined from…
The necessary and sufficient conditions for a class of functions $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$, where $q \geq 2$ is an even positive integer, have been recently identified for $q=4$ and $q=8$. In this article we give an…
Since the grand partition function $Z_q$ for the so-called $q$-particles (i.e.,\ quons), $q\in(-1,1)$, cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for $q=0$, and its…
Bent functions of the form $\mathbb{F}_2^n\rightarrow\mathbb{Z}_q$, where $q\geqslant2$ is a positive integer, are known as generalized bent (gbent) functions. Gbent functions for which it is possible to define a dual gbent function are…
In this paper, we further investigate properties of generalized bent Boolean functions from $\Z_{p}^n$ to $\Z_{p^k}$, where $p$ is an odd prime and $k$ is a positive integer. For various kinds of representations, sufficient and necessary…
It is known that partial spreads is a class of bent partitions. In \cite{AM2022Be,MP2021Be}, two classes of bent partitions whose forms are similar to partial spreads were presented. In \cite{AKM2022Ge}, more bent partitions $\Gamma_{1},…
In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering…