National Repository of Grey Literature 148 records found  1 - 10nextend  jump to record: Search took 0.00 seconds. 
Multiplication in a finite field of characteristic 2 and XOR-metrics
Carulkov, Nikita Edward ; Žemlička, Jan (advisor) ; Göloglu, Faruk (referee)
XOR-counts measure the efficiency of multiplication in finite fields of characteristic 2. In the first chapter we define two XOR-counts (the direct XOR-count and the sequential XOR-count) and present detailed proofs of some propositions from the paper from Lukas Kolsch about the XOR-counts of inverse matrices and permutation similar matrices. It seems that the case when the direct XOR-count is lower than the sequential XOR-count is rare. We will explore those cases in the second chapter. Some of them were already described in the paper from Lukas Kolsch and we prove that they occur only for matrices with order higher or equal to six. 1
Linear version of Holub's algorithm
Tvrdý, David ; Holub, Štěpán (advisor) ; Žemlička, Jan (referee)
This work studies a linear agorithm which decides if a given word is a fixed point of any nontrivial morphism. This work also contains a description of auxiliary data structures which are crucial for linear time complexity of the algorithm. A Java implementation of the algorithm is provided along with a step-by-step visualization for particular input words. 1
Generalized integral property
Hrúzová, Jana ; Žemlička, Jan (advisor) ; Příhoda, Pavel (referee)
This thesis is based on an article C. Boura and A. Canteaut, Another View of the Division Property, which is focused on division property of sets from Fn 2 . In this thesis we introduce important definitions and propositions about boolean function, polynomials and Reed-Muller codes at the beginning. Then we define parity set of a set from Fn 2 , which helps us to simplify the division property. We also show how sets, which satisfy division property of certain order, look like. From that we could follow how the division property propagate through the substitution-permutation network. 1
Testing the projectivity of modules
Matoušek, Cyril ; Šaroch, Jan (advisor) ; Žemlička, Jan (referee)
In this thesis, we study the problem of the existence of test modules for the projectivity. A right R-module is said to be a test module if it holds for every right R-module M that M is projective whenever T ∈ M⊥ . We show that test modules exist over right perfect rings, although their existence is not provable in ZFC in case of non-right perfect rings. In order to prove this, we use Shelah's uni- formization principle, which is independent of the axioms of ZFC. Furthermore, we show that test modules exist over rings of finite global dimension assuming the weak diamond principle, which is also independent of ZFC. 1
Rational linear dependencies of periodic points of the logistic map
Mik, Matěj ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
Period-n points of a polynomial f are roots, and hence elements of the splitting field, of the polynomial fn (x) − x, where fn denotes the nth iterate of f. In the thesis, we will focus on describing rational linear dependencies of period-n points of the polynomial f(x) = 4x(1 − x), which defines the so-called logistic map. We will present a description of the dependencies for n = 1, . . . , 5 and a partial result for n = 6. We will be using computer- calculated factorizations of polynomials over rational numbers and some finite field extensions. The factorizations will give us coordinates of the periodic points relative to some basis of their linear span, which will allow us to use a simple way of describing their dependencies. In the end of the thesis, we will put together an algorithm for describing the dependencies for a general n.
Short invertible elements in cyclotomic rings
Kroutil, Jaroslav ; Žemlička, Jan (advisor) ; Příhoda, Pavel (referee)
This bachelor's thesis is based on an article about the criterion for invertibility of elements in special- chosen cyclotomic rings. In this thesis, we start with defining important terms and statements from algebra that we need. Then we will deal with the existence of infinitely many prime numbers which satisfy conditions that are used for irreducible decomposition of cyclotomic polynomials. Based on this polynomials we define cyclotomic rings and at the end of this thesis we prove invertibility of elements from this rings depending on the size of their norm.
Descendants of Depolt - cadet branch of Premyslides
Ekrt, Tomáš ; Žemlička, Josef (advisor) ; Doležalová, Eva (referee)
Author in his bachelor's dissertation devote to cadet branch of Premyslides - descendants of Depolt. At first he sketch their genalogy, then he observe rank of each generation in the Czech Duchy and their fates. Then he also sketch what it meant to manage fief, what was significence of their land, and also their unhappy destiny in Silesian exile.
History of the Moravian branch of house Žerotín until the late Middle Ages.
Kamler, Jiří ; Bobková, Lenka (advisor) ; Žemlička, Josef (referee)
(in English): There are not many of the original Moravian noble families that have been ranked among the high nobility in history. One of them is the Žerotín family, whose origins and development until the beginning of the 15th century is devoted to the following work. The first written mention of the family comes from the end of the 12th century, when their connection to the Moravian Margrave or the Czech King, typical for the nobility, is already evident. In the 13th century, the first phase of the expansion of family possessions and the expansion of the original family of Bludovicové into two branches - jičínská, which at the beginning of the 14th century died out and the šumvaldská, which in the 14th century acquired the village of Žerotín, after which the family later wrote. Throughout the period under review, the family did not exceed the Morava region, but in several cases it managed to assert itself into the structures of the provincial administration, whether in the administration of landlords or in the judicial area, etc. The ancestors of the Žerotín family did not stand aside and their contacts with the prominent ecclesiastical and religious communities, secular representatives of Moravia, or the whole kingdom, were evident, though sometime sporadically. In the course of the 14th...
Modules over string algebras
Löwit, Jakub ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The aim of this thesis is to investigate the categories of modules over the so called string algebras. In particular, we try to understand the cotorsion pairs in these categories, which boils down to understanding the decompositions of extensions of such modules. For string algebras with some oriented tree for the underlying quiver, we describe some classes given by these cotorsion pairs in terms of purely combinatorial closure properties. For any string algebras, the combinatorics appears to be similar, althought more complicated.
LWE and provably secure key exchange schemes
Václavek, Jan ; Příhoda, Pavel (advisor) ; Žemlička, Jan (referee)
The threat of large-scale quantum computers motivates cryptographers to base cryptosystems on problems believed to be resistant against quantum computers. In this thesis, we focus on the LWE problem which is believed to be resistant against quantum computers. First, we describe lattices which are closely related to the LWE problem. We introduce basic notions, describe lattice problems and solve exercises related to the covering radius of lattice. After that, we introduce the LWE problem and its variants. We prove reductions from two lattice problems to certain variant of the LWE problem. We define the notion of statistical distance and prove some lemmata about it which we need within reductions. Moreover, we show concrete application of the LWE problem. We describe a scheme for key exchange and briefly prove its security under the assumption that the LWE problem is hard. 1

National Repository of Grey Literature : 148 records found   1 - 10nextend  jump to record:
See also: similar author names
1 Žemlička, Jakub
2 Žemlička, Jan
9 Žemlička, Josef
Interested in being notified about new results for this query?
Subscribe to the RSS feed.