Vectorial bent functions with non-weakly regular components

Name: Vectorial bent functions with non-weakly regular components
Author: Meidl, W., Cesmelioglu, Ayca

İsim	Vectorial bent functions with non-weakly regular components
Yazar	Meidl, W., Cesmelioglu, Ayca
Basım Tarihi:	2024-12
Basım Yeri	- IEEE
Konu	Weight distribution of linear codes, Walsh transform, Non-dual bent functions, Non-weakly regular bent functions, Vectorial bent functions
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0018-9448
Kayıt Numarası	d1b5e82a-7886-4448-ad7a-bd45b3950ea6
Lokasyon	Natural and Mathematical Sciences
Tarih	2024-12
Notlar	Austrian Science Fund (FWF)
Örnek Metin	It is shown that the generalized Rothaus construction of p-ary bent functions can be extended to a construction of a vectorial bent function with non-weakly regular components, for which in general the duals are not a bent function, i.e., they belong to the class of non-dual bent functions. This complements results on other two constructions of non-weakly regular bent functions, the generalized Maiorana-McFarland construction and the semi-direct sum, for which vectorial versions are presented and the properties of their duals are investigated in the literature. The distribution of the values of the Walsh transform of vectorial bent functions (with non-weakly regular components) is then analysed in detail. Among others, a condition on the values of the Walsh transform of a vectorial bent function from F-p(n) to F-p(m) is presented, which implies that m <= [n/2]. This refines a classical result by Nyberg, which states that for an (n, m) bent function, n even, with only regular components, m can be at most n/2. Some results on the weight distribution of codes obtained from vectorial bent functions with non-weakly regular components complement the article.
DOI	10.1109/TIT.2024.3434481
Cilt	70

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Vectorial bent functions with non-weakly regular components

Yazar Meidl, W., Cesmelioglu, Ayca

Basım Tarihi 2024-12

Basım Yeri - IEEE

Konu Weight distribution of linear codes, Walsh transform, Non-dual bent functions, Non-weakly regular bent functions, Vectorial bent functions

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0018-9448

Kayıt Numarası d1b5e82a-7886-4448-ad7a-bd45b3950ea6

Lokasyon Natural and Mathematical Sciences

Tarih 2024-12

Notlar Austrian Science Fund (FWF)

Örnek Metin It is shown that the generalized Rothaus construction of p-ary bent functions can be extended to a construction of a vectorial bent function with non-weakly regular components, for which in general the duals are not a bent function, i.e., they belong to the class of non-dual bent functions. This complements results on other two constructions of non-weakly regular bent functions, the generalized Maiorana-McFarland construction and the semi-direct sum, for which vectorial versions are presented and the properties of their duals are investigated in the literature. The distribution of the values of the Walsh transform of vectorial bent functions (with non-weakly regular components) is then analysed in detail. Among others, a condition on the values of the Walsh transform of a vectorial bent function from F-p(n) to F-p(m) is presented, which implies that m <= [n/2]. This refines a classical result by Nyberg, which states that for an (n, m) bent function, n even, with only regular components, m can be at most n/2. Some results on the weight distribution of codes obtained from vectorial bent functions with non-weakly regular components complement the article.

DOI 10.1109/TIT.2024.3434481

Cilt 70