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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 75 for “"finite field"”.
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Correct-by-construction finite field arithmetic in Coq
… statement is especially true for the specialized finite-field libraries used for ECC code, resulting in frequent implementation bugs. I describe the methodologies used to create a Coq framework that generates implementations of finite-field arithmetic routines along with proofs of their …
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Arithmetic and analytic properties of finite field hypergeometric functions
… arithmetic and analytic properties of Gaussian (finite field) hypergeometric series. We present expressions for the number of F,-points on certain families of varieties as special values of these functions. We also present "hypergeometric trace formulas" for the traces of Hecke operators on …
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Visual system analysis through use of finite field sine gratings.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering, 1973
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On the Use of Finite Field Based Modeling in Polynomial Manipulation
Made available in DSpace on 2014-12-08T22:24:29Z (GMT). No. of bitstreams: 1 6901402.pdf: 3093978 bytes, checksum: 030e2670fc45221c81dd5839e7f50313 (MD5) Previous issue date: 1968
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Explicit Factorization of Generalized Cyclotomic Polynomials of Order $2^m 3$ Over a Finite Field $F_q$
… of order $2^m 3$, $Q_{2^m3,a}(x)$, over a finite field $F_q$ with $q$ elements where $q$ is a prime power, $m$ is a nonnegative integer and $a$ is a nonnegative element of $F_q$. We use the relation between usual cyclotomic polynomials and $a$-cyclotomic polynomials. Factorizations split …
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The derived category of representations of the special linear group of degree two over a finite field
… of the special linear group of degree two over a finite field in defining characteristic. In particular, we study the automorphisms of derived category of representations. We have been able to obtain a new type of autoequivalence. This autoequivalence has some uncommon features. It is more …
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René Schoof's Algorithm for Determining the Order of the Group of Points on an Elliptic Curve over a Finite Field
… 300 years. In addition, elliptic curves over finite fields find practical application in the areas of cryptography and coding theory. For such problems, knowing the order of the group of points satisfying the elliptic curve equation is important to the security of these applications. In 1985 …
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Rational Points on Lattice Varieties
… Witt vectors with algebraically closed residue field in prime characteristic. These varieties are defined over a finite field. For varieties over finite field, the local zeta function encapsulates valuable number-theoretic information about the variety. We calculate explicitly the zeta functions …
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The Minimum Rank Problem Over Finite Fields
… graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal forbidden subgraphs for any field. Our second main result is a structural characterization of all graphs having minimum rank at …
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Construção de códigos de bloco lineares via transformadas digitais
… finitos (Códigos FFCT tipo 4 par, do inglês finite field cosine transform, e Códigos FFST tipo 4 par, do inglês finite field sine transform), são apresentadas nesta dissertação. A matriz de paridade de cada código, sua dimensão e distância mínima são obtidas a partir da autoestrutura da …
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General Factoring Algorithms for Polynomials over Finite Fields
… for factoring polynomials with coefficients in finite fields. In particular, we develop one deterministic algorithm due to Elwyn Berlekamp and one probabilistic algorithm due to David Cantor and Hans Zassenhaus. While some authors present versions of the algorithms that can only factor …
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Trellis Decoding And Applications For Quantum Error Correction
… error for any stabilizer code over a finite field of prime dimension. We define a canonical form for the stabilizer group and use it to classify the internal structure of the graph. Similarities and differences between the classical and quantum theories are discussed throughout. …
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L-functions of twisted elliptic curves over function fields
… curves and their L-functions over number fields, in particular over the rational numbers. Much less work has been done over function fields, especially computationally, where the underlying geometry of the function field plays an intimate role in the arithmetic of elliptic curves. We make …
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The ring of invariants of the orthogonal group over finite fields in odd characteristic
Let $V$ be a non-zero finite dimensional vector space over a finite field $\mathbb{F}_q$ of odd characteristic. Fixing a non-singular quadratic form $\xi_0$ in $S^2(V^*)$, the symmetric square of the dual of V we are concerned with the Orthogonal group $O(\xi_0)$, the subgroup of the General Linear …
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Multilinear operators in harmonic analysis: Methods and applications
… bilinear Hilbert transform along polynomials, finite field version of bilinear Radon transform, a hybrid of bilinear Hilbert transform and the paraproduct, etc. Our aim is to find operator norms of these operators: showing that they are finite or have certain decay. Applications in Roth type …
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High Speed and Low-Complexity Hardware Architectures for Elliptic Curve-Based Crypto-Processors
… efficient and low-complexity architectures for finite field multiplications over Gaussian normal basis (GNB). We propose three new low-complexity digit-level architectures for finite field multiplication. Architectures are modified in order to make them more suitable for hardware implementations …
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Nearby cycles and the cohomology of shtukas
… forms for any reductive group over a function field using excursion operators. Our aim is to give a general approach for proving certain local-global compatibilities satisfied by these Langlands parameters. The main consequence for the Langlands correspondence is to show that Lafforgue's …
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On network coding capacity : matroidal networks and network capacity regions
One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity regions. In our matroidal approach, we prove the converse …
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Isotropic graphs with applications to parallel computation
… explicit construction techniques, based on finite fields, that provide graphs which exhibit good expansion properties at low densities and can be efficiently implemented. These techniques are related to the one introduced by Morgenstern, based on quotients of the projective linear group over …
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