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    Almost perfect autocorrelation sequences with small number of pauses for applications in magnetic resonance
    (Springer, 2024) Tekin, Eda; Gnilke, Oliver Wilhelm; Ozbudak, Ferruh; Bluemich, Bernhard; Greferath, Marcus
    It is well known that it is a challenge to find constant amplitude sequences with perfect autocorrelation over small alphabets. In this work we present a construction that provides sequences with perfect cyclic autocorrelation over different alphabets using the value zero only once or twice in their period. The constructions provide a big variety of periods also at moderate lengths and the corresponding sequences may be considered to be of 'almost' constant amplitude. These sequences have applications in NMR spectroscopy with low excitation power.
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    Classification of a Sequence Family Using Plateaued Functions
    (Ieee, 2017) Boztas, Serdar; Ozbudak, Ferruh; Tekin, Eda
    The design of CDMA sequence families using quadratic functions dates hack to Gold sequences from the 1960s. Since then there have been a number of different such designs with good correlation properties, some optimal and some near optimal, and the term Gold-like is usually used to denote such sequences. In this paper we use the concept of plateaued functions, not necessarily quadratic, in order to classify such sequence families and present some examples in this direction which depend on the characteristic p and degree n of the Galois field 4, used to define the sequences.
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    A Complementary Result on the Construction of Quadratic Cyclotomic Classes
    (Springer International Publishing Ag, 2022) Otal, Kamil; Tekin, Eda
    Side-channel analysis (SCA) is a general name for cryptanalytic methods based on side information gathered by measuring and analyzing of various physical parameters. Threshold implementation (TI) is one of the successful countermeasure techniques for some types of SCA. Within this scope, Nikova et al. gave an algorithm on the decomposition of power permutations into quadratic power permutations over finite fields F2n in [Cryptogr. Commun. 11, 37-384 (2019)]. Later on, Otal and Tekin gave a sufficient way in [Cryptogr. Commun. 13, 837-845 (2021)] to reduce the precomputation cost in the algorithm of Nikova et al. substantially. In this paper, we prove that this sufficient way is also necessary, in other words, the proposed way is an optimal solution. In that way, we provide a complementary result on the construction of quadratic cyclotomic classes.
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    CORRELATION DISTRIBUTION OF A SEQUENCE FAMILY GENERALIZING SOME SEQUENCES OF TRACHTENBERG
    (Amer Inst Mathematical Sciences-Aims, 2021) Ozbudak, Ferruh; Tekin, Eda
    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 family has p(n) + 1 cyclically distinct sequences with period p(n) - 1. We compute the exact correlation distribution of the function g(x) with linear m-sequences and amongst themselves. The cross-correlation values are obtained as C-i,C-j(tau) is an element of {-1, -1 +/- p(n+e/2), -1 + p(n)}.
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    Efficient generation of quadratic cyclotomic classes for shortest quadratic decompositions of polynomials
    (Springer, 2021) Otal, Kamil; Tekin, Eda
    Nikova et al. investigated the decomposition problem of power permutations over finite fields F-2n in (Cryptogr. Commun. 11:379-384, 2019). In particular, they provided an algorithm to give a decomposition of a power permutation into quadratic power permutations. Their algorithm has a precomputation step that finds all cyclotomic classes of F-2n and then use the quadratic ones. In this paper, we provide an efficient and systematic method to generate the representatives of quadratic cyclotomic classes and hence reduce the complexity of the precomputation step drastically. We then apply our method to extend their results on shortest quadratic decompositions of x(2n-2) from 3 <= n <= 16 to 3 <= n <= 24 and correct a typo (for n = 11). We also give two explicit formulas for the time complexity of the adaptive search to understand its efficiency with respect to the parameters.
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    Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions
    (Ieee-Inst Electrical Electronics Engineers Inc, 2018) Boztas, Serdar; Ozbudak, Ferruh; Tekin, Eda
    The design of code division multiple access sequence families dates back to the Gold sequences from the 1960s. Since then there has been a number of different such designs with good correlation properties, some optimal and some near-optimal. In this paper, we use the concept of plateaued functions with arbitrary degree, in order to compute their full correlation distributions. First, we give an explicit correlation distribution of a sequence family using a non-quadratic function. Then for the quadratic functions, we present a general classification of Gold-like sequence families for all possible characteristics p and degrees n of the Galois field F-pn used to define the sequences. We are able to obtain the full correlation distribution of the families we consider. This paper also uses techniques from the theory of algebraic curves in order to obtain some of the results.
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    Generalized nonbinary sequences with perfect autocorrelation, flexible alphabets and new periods
    (Springer, 2018) Boztas, Serdar; Ozbudak, Ferruh; Tekin, Eda
    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 alternatives for wireless communications and radar system designers for applications in ranging and synchronisation as well as channel identification.
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    Moments of the support weight distribution of linear codes
    (Springer, 2013) Ozen, Ibrahim; Tekin, Eda
    In this work, we give the expectation and the covariance formulas for the support weight distributions of linear codes.
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    New Correlations of m-sequences over the finite field F4 compatible with a new bijection to Z4
    (Ieee, 2022) Boztas, Serdar; Ozbudak, Ferruh; Tekin, Eda
    In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F(4)n to F-4. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation.
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    A New Method to Compute Sequence Correlations Over Finite Fields
    (Ieice-Inst Electronics Information Communication Engineers, 2023) Boztas, Serdar; Ozbudak, Ferruh; Tekin, Eda
    In this paper we obtain a new method to compute the correlation values of two arbitrary sequences defined by a mapping from F4n to F4. We apply this method to demonstrate that the usual nonbinary maximal length sequences have almost ideal correlation under the canonical complex correlation definition and investigate some decimations giving good cross correlation. The techniques we develop are of independent interest for future investigation of sequence design and related problems, including Boolean functions.
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    Rastsal kodların destek ağırlıklarının istatistikleri
    (Karabük Üniversitesi, 2012) Tekin, Eda; Nallı, Ayşe; Dikmen, Can Murat
    Bu tezde öncelikle kod tanımı, kodlama teorisinde çok önemli yeri olan lineer kodlar, parametreleri ve özellikleri incelenmiş, daha sonra genelleştirilmiş lineer kod tanımı verilip parametreleri incelenmiştir. Çalışmamızın 5. bölümünde, genelleştirilmiş kodlar için, kxn lik bir matrisin rankının r olma olasılığı formülünden yararlanılarak bu matrisin beklenti formülü, beklenti formülünden yararlanılarak farklı I ve J alt matrislerine karşılık gelen rank fonksiyonlarının kovaryansları, destek ağırlık polinomunun beklentisi, ve son olarak bir C [n,k] kodunun destek ağırlıkları arasındaki kovaryans formülleri elde edildi. Son bölümde ise lineer olmayan bir kod: Fibonacci koduna değinildi.