Ferruh Özbudak

Department of Mathematics
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Two or Three Weight Linear Codes from Non-Weakly Regular Bent Functions
Özbudak, Ferruh; Pelen, Rumi Melih (2022-05-01)
© 1963-2012 IEEE.Linear codes with few weights have applications in consumer electronics, communications, data storage systems, secret sharing, authentication codes, and association schemes. As a special class of linear co...
Complete b-symbol weight distribution of some irreducible cyclic codes
Zhu, Hongwei; Shi, Minjia; Özbudak, Ferruh (2022-05-01)
Recently, b-symbol codes are proposed to protect against b-symbol errors in b-symbol read channels. It is an interesting subject of study to consider the complete b-symbol weight distribution of cyclic codes since b-symbol...
Imprimitive symmetric association schemes of classes 5 and 6 arising from ternary non-weakly regular bent functions
Özbudak, Ferruh; Pelen, Rumi Melih (2022-04-01)
Let F be a ternary non-weakly regular bent function in GMMF class whose dual F* is bent. We prove that if F satisfies certain conditions, then collecting the pre-image sets of the dual function F* with respect to the subse...
Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes
Koese, Seyda; Özbudak, Ferruh (2022-03-01)
We determine the unique factorization of some polynomials over a finite local commutative ring with identity explicitly. This solves and generalizes the main conjecture of Qian, Shi and Sole in [13]. We also give some appl...
LCD codes from tridiagonal Toeplitz matrices
Shi, Minjia; Özbudak, Ferruh; Xu, Li; Solé, Patrick (2021-10-01)
Double Toeplitz (DT) codes are codes with a generator matrix of the form (I,T) with T a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When T is tridiagonal and symmetric we determine its s...
Correlation distribution of a sequence family generalizing some sequences of trachtenberg
Özbudak, Ferruh (2021-08-01)
In this paper, we give a classification of a sequence family, over arbitrary characteristic, adding linear trace terms to the function g(x) = Tr(x(d)), where d = p(2k) - p(k) + 1, first introduced by Trachtenberg. The fami...
New generalized almost perfect nonlinear functions
Özbudak, Ferruh (2021-02-01)
APN (almost perfect non-linear) functions over finite fields of even characteristic are widely studied due to their applications to the design of symmetric ciphers resistant to differential attacks. This notion was recentl...
Hermitian Rank Metric Codes and Duality
La Cruz, Javier De; Evilla, Jorge Robinson; Özbudak, Ferruh (2021-01-01)
In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for F-q2-linear matrix codes in the ambient space (F-q2)(n,m) and for both F-q2-additive codes and F-q2m-linear code...
Geometric Approach to b-Symbol Hamming Weights of Cyclic Codes
Shi, Minjia; Özbudak, Ferruh; Sole, Patrick (2021-01-01)
IEEESymbol-pair codes were introduced by Cassuto and Blaum in 2010 to protect pair errors in symbol-pair read channels. Recently Yaakobi, Bruck and Siegel (2016) generalized this notion to b-symbol codes in order to consid...
Secondary constructions of (non)weakly regular plateaued functions over finite fields
Mesnager, Sihem; Özbudak, Ferruh; Sinak, Ahmet (2021-01-01)
Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We...
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