Strongly regular graphs arising from non-weakly regular bent functions

2019-11-01
In this paper, we study two special subsets of a finite field of odd characteristics associated with non-weakly regular bent functions. We show that those subsets associated to non-weakly regular even bent functions in the GMMF class (see cesmelioglu et al. Finite Fields Appl. 24, 105-117 2013) are never partial difference sets (PDSs), and are PDSs if and only if they are trivial subsets. Moreover, we analyze the two known sporadic examples of non-weakly regular ternary bent functions given in Helleseth and Kholosha (IEEE Trans. Inf. Theory 52(5), 2018-2032 2006, Cryptogr. Commun. 3(4), 281-291 2011). We observe that corresponding subsets are non-trivial partial difference sets. We show that they are the union of some cyclotomic cosets and so correspond to 2-class fusion schemes of a cyclotomic scheme. We also present a further construction giving non-trivial PDSs from certain p-ary functions which are not bent functions.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES

Suggestions

Generalized nonbinary sequences with perfect autocorrelation, flexible alphabets and new periods
BOZTAŞ, Serdar; Özbudak, Ferruh; TEKİN, Eda (Springer Science and Business Media LLC, 2018-05-01)
We extend the parameters and generalize existing constructions of perfect autocorrelation sequences over complex alphabets. In particular, we address the PSK+ constellation (Boztas and Udaya 2010) and present an extended number theoretic criterion which is sufficient for the existence of the new sequences with perfect autocorrelation. These sequences are shown to exist for nonprime alphabets and more general lengths in comparison to existing designs. The new perfect autocorrelation sequences provide novel a...
Almost p-ary sequences
Ozden, Busra; Yayla, Oğuz (Springer Science and Business Media LLC, 2020-11-01)
In this paper we study almost p-ary sequences and their autocorrelation coefficients. We first study the number l of distinct out-of-phase autocorrelation coefficients for an almost p-ary sequence of period n + s with s consecutive zero-symbols. We prove an upper bound and a lower bound on l. It is shown that l can not be less than min{s,p,n}. In particular, it is shown that a nearly perfect sequence with at least two consecutive zero symbols does not exist. Next we define a new difference set, partial dire...
Isomorphism classes of elliptic curves over finite fields of characteristic two
Kırlar, Barış Bülent; Akyıldız, Ersan; Department of Mathematics (2005)
In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphi...
NONCOMMUTATIVE MACKEY THEOREM
Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01)
In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
On affine variety codes from the Klein quartic
Geil, Olav; Özbudak, Ferruh (Springer Science and Business Media LLC, 2019-03-01)
We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433-464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and HOholdt, IEEE Trans. Inform. The...
Citation Formats
F. Özbudak, “Strongly regular graphs arising from non-weakly regular bent functions,” CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, pp. 1297–1306, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37529.