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Showing 1 to 20 of 61 for “"finite fields"”.
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Elliptic Curves Over Finite Fields
… on the the theory of elliptic curves over finite fields. In Chapter 1, affine and projective planes are introduced. Chapter 2 introduces the theory of algebraic curves and the Weierstrass Normal Form of a cubic curve is derived. In Chapter 3 we define derivations on arbitrary polynomial …
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Primitive Elements in Finite Fields
Made available in DSpace on 2015-09-28T15:19:48Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3153400.pdf: 2638455 bytes, checksum: f36c631d1df9b18c8543057bd2169071 (MD5) Previous issue date: 2004
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Monomial Dynamical Systems over Finite Fields
… is an important problem in the theory of finite dynamical systems. For monomial dynamical systems, that is, a system that can be described by monomials, information about the limit cycles can be obtained from the monomials themselves. In particular, this work contains sufficient and …
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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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Trace Forms Over Finite Fields of Characteristic Two
… provides elementary facts about trace forms over finite fields of characteristic two in order to generalize some results concerning Gold functions. Then determines new set of maximal Artin-Schreier curves with possible pair of invariants, finds possible trace forms with specific co-dimemntion and …
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Multiple bit error correcting architectures over finite fields
This thesis proposes techniques to mitigate multiple bit errors in GF arithmetic circuits. As GF arithmetic circuits such as multipliers constitute the complex and important functional unit of a crypto-processor, making them fault tolerant will improve the reliability of circuits that are employed …
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Covering Systems of Polynomial Rings Over Finite Fields
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n …
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Existence problems of primitive polynomials over finite fields
… concerns existence of primitive polynomials over finite fields with one coefficient arbitrarily prescribed. It completes the proof of a fundamental conjecture of Hansen and Mullen (1992), which asserts that, with some explicable general exceptions, there always exists a primitive polynomial of any …
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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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The number of zeros of linear recurring sequences over finite fields
… a homogeneous linear recurring sequence over a finite field of <italic>q<italic> elements, based on an irreducible minimal polynomials of degree <italic>d<italic> and order <italic>m<italic> as the characteristic polynomial. I prove upper and lower bounds on the cardinality of the set of number …
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Algorithms for Finite Dimensional Algebras Over Finite Fields Using Basic Algebras
… algorithms for computing information about finite dimensional associative algebra over a finite field. In particular, we provide algorithms for computing a basis, the lattice of two-sided ideals, the center, and the unit group for a finite dimensional associative algebra over a finite …
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Application of Fourier Transform Over Finite-Fields to Error-Correcting Codes
Made available in DSpace on 2014-12-10T19:07:20Z (GMT). No. of bitstreams: 1 7500279.pdf: 2583193 bytes, checksum: 9b74718ca8182c99c84564311303cad1 (MD5) Previous issue date: 1974
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Arboreal representations, sectional monodromy groups, and abelian varieties over finite fields
This thesis consists of three independent parts. The first part studies arboreal representations of Galois groups - an arithmetic dynamics analogue of Tate modules - and proves some large image results, in particular confirming a conjecture of Odoni. Given a field K, a separable polynomial …
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A q-analogue of spanning trees : nilpotent transformations over finite fields
The main result of this work is a q-analogue relationship between nilpotent transformations and spanning trees. For example, nilpotent endomorphisms on an n-dimensional vector space over Fq is a q-analogue of rooted spanning trees of the complete graph Kn. This relationship is based on two similar …
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Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields
… problem of finding the number of matrices over a finite field with a certain rank and with support that avoids a subset of the entries. These matrices are a q-analogue of permutations with restricted positions (i.e., rook placements). Extending a result of Haglund, we show that when the set of …
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Multiple access networks over finite fields : optimality of separation, randomness and linearity
… transmit and noise alphabets belong to a finite field. We show that source-channel separation holds when the additive noise is independent of inputs. However, for input-dependent noise, separation may not hold. For channels over the binary field, we derive the expression for the …
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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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Construction of the orthogonal groups of n x n circulant matrices over finite fields
Let F be a finite field with q elements where $q=p\sp{m}, p$ prime. Let ${\cal M}$ be the algebra of n x n circulant matrices over F. The set $O\sb{(n,q)}$ of orthogonal n x n circulant matrices is a subgroup of ${\cal M}\sp\times.$ The major purposes of the thesis are: (1) to explain K. A. Byrd …
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