Ferruh Özbudak

Department of Mathematics
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Additive cyclic complementary dual codes over F4
Shi, Minjia; Liu, Na; Özbudak, Ferruh; Solé, Patrick (2022-10-01)
© 2022 Elsevier Inc.An additive cyclic code of length n over F4 can be defined equivalently as an F2[x]/〈xn+1〉-submodule of F4[x]/〈xn+1〉. In this paper we study additive cyclic and complementary dual codes of odd length ov...
Classification of permutation polynomials of the form x3g(xq-1) of Fq2 where g(x) = x3+ bx+ c and b,c∈Fq∗
Özbudak, Ferruh; Gülmez Temür, Burcu (2022-07-01)
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.We classify all permutation polynomials of the form x3g(xq-1) of Fq2 where g(x) = x3+ bx+ c and b,c∈Fq∗. Moreo...
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...
Covering Radius of Melas Codes
Shi, Minjia; Helleseth, Tor; Özbudak, Ferruh; Sole, Patrick (2022-01-01)
IEEEWe prove that the covering radius of the Melas code M(m, q) of length n = qm - 1 over Fq is 2 if q > 3. We also prove that the covering radius of M(m, 3) is 3 is m ≥ 3, the covering radius of M(2, 3) is 4...
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...
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