On affine variety codes from the Klein quartic

Geil, Olav
Özbudak, Ferruh
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. Theory 46(2), 635-641, 2000 and HOholdt 1998) from Grobner basis theory and for this purpose we develop a new method where we inspired by Buchberger's algorithm perform a series of symbolic computations.


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...
Results on symmetric S-boxes constructed by concatenation of RSSBs
KAVUT, SELÇUK; Baloglu, Sevdenur (Springer Science and Business Media LLC, 2019-07-01)
In this paper, we first present an efficient exhaustive search algorithm to enumerate 6 x 6 bijective S-boxes with the best-known nonlinearity 24 in a class of S-boxes that are symmetric under the permutation (x) = (x(0), x(2), x(3), x(4), x(5), x(1)), where x = (x(0), x1,...,x5)?26. Since any S-box S:?26?26 in this class has the property that S((x)) = (S(x)) for every x, it can be considered as a construction obtained by the concatenation of 5 x 5 rotation-symmetric S-boxes (RSSBs). The size of the search ...
Strongly regular graphs arising from non-weakly regular bent functions
Özbudak, Ferruh (Springer Science and Business Media LLC, 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...
A concatenated construction of linear complementary pair of codes
GÜNERİ, CEM; Özbudak, Ferruh; Sacikara, Elif (Springer Science and Business Media LLC, 2019-09-01)
A concatenated construction for linear complementary dual codes was given by Carlet et al. using the so-called isometry inner codes. Here, we obtain a concatenated construction to the more general family, linear complementary pair of codes. Moreover, we extend the dual code description of Chen et al. for concatenated codes to duals of generalized concatenated codes. This allows us to use generalized concatenated codes for the construction of linear complementary pair of codes.
On equivariant Serre problem for principal bundles
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2018-08-01)
Let E-G be a Gamma-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Gamma, where G and Gamma are complex linear algebraic groups. Suppose X is contractible as a topological Gamma-space with a dense orbit, and x(0) is an element of X is a Gamma-fixed point. We show that if Gamma is reductive, then E-G admits a Gamma-equivariant isomorphism with the product principal G-bundle X x rho E-G(x(0)), where rho : Gamma -> G is a homomorphism between algebraic...
Citation Formats
O. Geil and F. Özbudak, “On affine variety codes from the Klein quartic,” CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, pp. 237–257, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48660.