Thesis (M.S.)--University of North Carolina at Wilmington, 2006. / Includes bibliographical references (leaf: [42])

In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5. / by Nicola Pace. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / System requirements: Adobe Reader. / Mode of access: World Wide Web.

Yeung Wai Ling Winnie. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 99-100). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Finite Fields --- p.4 / Chapter 2.1 --- Basic Properties of Finite Fields --- p.4 / Chapter 2.2 --- Existence and Uniqueness of Finite Fields --- p.8 / Chapter 2.3 --- Algorithms in Factoring Polynomials --- p.11 / Chapter 2.3.1 --- Factorization of xn ´ؤ 1 --- p.11 / Chapter 2.3.2 --- Berlekamp Algorithm for Factorizing an Arbitrary Polynomial --- p.13 / Chapter 3 --- Algebraic Curves --- p.17 / Chapter 3.1 --- Affine and Projective Curves --- p.17 / Chapter 3.2 --- Local Properties and Intersections of Curves --- p.19 / Chapter 3.3 --- Linear Systems of Curves and Noether's Theorem --- p.24 / Chapter 3.4 --- Rational Function and Divisors --- p.29 / Chapter 3.5 --- Differentials on a Curve --- p.34 / Chapter 3.6 --- Riemann-Roch Theorem --- p.36 / Chapter 4 --- Coding Theory --- p.46 / Chapter 4.1 --- Introduction to Coding Theory --- p.46 / Chapter 4.1.1 --- Basic Definitions for Error-Correcting Code --- p.46 / Chapter 4.1.2 --- Geometric Approach to Error-Correcting Capabilities of Codes --- p.48 / Chapter 4.2 --- Linear Codes --- p.49 / Chapter 4.2.1 --- The Dual of a Linear Code --- p.54 / Chapter 4.2.2 --- Syndrome Decoding --- p.57 / Chapter 4.2.3 --- Extension of Basic Field --- p.60 / Chapter 4.3 --- The Main Problem in Coding Theory --- p.62 / Chapter 4.3.1 --- "Elementary Results on Aq(n, d)" --- p.63 / Chapter 4.3.2 --- "Lower Bounds on Aq(n, d)" --- p.63 / Chapter 4.3.3 --- "Upper Bounds on Aq(n,d)" --- p.65 / Chapter 4.3.4 --- Asymptotic Bounds --- p.67 / Chapter 4.4 --- Rational Codes --- p.68 / Chapter 4.4.1 --- Hamming Codes --- p.68 / Chapter 4.4.2 --- Codes on an Oval --- p.69 / Chapter 4.4.3 --- Codes on a Twisted Cubic Curve --- p.78 / Chapter 4.4.4 --- Normal Rational Codes --- p.82 / Chapter 4.5 --- Goppa Codes --- p.84 / Chapter 4.5.1 --- Classical Goppa Codes --- p.85 / Chapter 4.5.2 --- Geometric Goppa Codes --- p.88 / Chapter 4.5.3 --- Good Codes from Algebraic Geometry --- p.91 / Chapter 4.6 --- A Recent Non-linear Code Improving the Tsfasman- Vladut-Zink Bound --- p.93 / Bibliography --- p.99

by Chiu Chak Lam. / Thesis submitted in: June, 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 67-69). / Abstract also in Chinese. / Chapter 1 --- Basic Knowledge of Elliptic Curve --- p.2 / Chapter 1.1 --- Elliptic Curve Group Law --- p.2 / Chapter 1.2 --- Discriminant and j-invariant --- p.7 / Chapter 1.3 --- Elliptic Curve over C --- p.10 / Chapter 1.4 --- Complex Multiplication --- p.15 / Chapter 2 --- Order of Elliptic Curve Group Over Finite Fields and the Endo- morphism Ring --- p.18 / Chapter 2.1 --- Hasse's Theorem --- p.18 / Chapter 2.2 --- The Torsion Group --- p.23 / Chapter 2.3 --- The Weil Conjectures --- p.33 / Chapter 3 --- Computing the Order of an Elliptic Curve over a Finite Field --- p.35 / Chapter 3.1 --- Schoof's Algorithm --- p.35 / Chapter 3.2 --- Computation Formula --- p.38 / Chapter 3.3 --- Recent Works --- p.42 / Chapter 4 --- Primality Test Using Elliptic Curve --- p.43 / Chapter 4.1 --- Goldwasser-Kilian Test --- p.43 / Chapter 4.2 --- Atkin's Test --- p.44 / Chapter 4.3 --- Binary Quadratic Form --- p.49 / Chapter 4.4 --- Practical Consideration --- p.51 / Chapter 5 --- Elliptic Curve Factorization Method --- p.54 / Chapter 5.1 --- Lenstra's method --- p.54 / Chapter 5.2 --- Worked Example --- p.56 / Chapter 5.3 --- Practical Considerations --- p.56 / Chapter 6 --- Elliptic Curve Public Key Cryptosystem --- p.59 / Chapter 6.1 --- Outline of the Cryptosystem --- p.59 / Chapter 6.2 --- Index Calculus Method --- p.61 / Chapter 6.3 --- Weil Pairing Attack --- p.63

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Gary L. Ebert, Dept. of Mathematical Sciences. Includes bibliographical references.

Paper 1. This paper establishes several algebraic embedding theorems, each of which asserts that a certain kind of residuated structure can be embedded into a richer one. In almost all cases, the original structure has a compatible involution, which must be preserved by the embedding. The results, in conjunction with previous findings, yield separative axiomatizations of the deducibility relations of various substructural formal systems having double negation and contraposition axioms. The separation theorems go somewhat further than earlier ones in the literature, which either treated fewer subsignatures or focussed on the conservation of theorems only. Paper 2. It is proved that the variety of relevant disjunction lattices has the finite embeddability property (FEP). It follows that Avron’s relevance logic RMImin has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron’s result that RMImin is decidable. Paper 3. An idempotent residuated po-monoid is semiconic if it is a subdirect product of algebras in which the monoid identity t is comparable with all other elements. It is proved that the quasivariety SCIP of all semiconic idempotent commutative residuated po-monoids is locally finite. The lattice-ordered members of this class form a variety SCIL, which is not locally finite, but it is proved that SCIL has the FEP. More generally, for every relative subvariety K of SCIP, the lattice-ordered members of K have the FEP. This gives a unified explanation of the strong finite model property for a range of logical systems. It is also proved that SCIL has continuously many semisimple subvarieties, and that the involutive algebras in SCIL are subdirect products of chains. Paper 4. Anderson and Belnap’s implicational system RMO can be extended conservatively by the usual axioms for fusion and for the Ackermann truth constant t. The resulting system RMO is algebraized by the quasivariety IP of all idempotent commutative residuated po-monoids. Thus, the axiomatic extensions of RMO are in one-to-one correspondence with the relative subvarieties of IP. It is proved here that a relative subvariety of IP consists of semiconic algebras if and only if it satisfies x (x t) x. Since the semiconic algebras in IP are locally finite, it follows that when an axiomatic extension of RMO has ((p t) p) p among its theorems, then it is locally tabular. In particular, such an extension is strongly decidable, provided that it is finitely axiomatized. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2008.

Includes bibliography. / 281 p ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--Dept. of Pure Mathematics, University of Adelaide, 1978

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Bibliography: p. 101-103.