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Optimal ternary linear codesJones, Christopher Martin January 2000 (has links)
No description available.
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Some properties of arcs, caps and quadrics in projective spaces in finite orderVereecke, Sam K. J. January 1998 (has links)
No description available.
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Partial ordering of weak mutually unbiased bases in finite quantum systemsOladejo, Semiu Oladipupo January 2015 (has links)
There has being an enormous work on finite quantum systems with variables in Zd, especially on mutually unbiased bases. The reason for this is due to its wide areas of application. We focus on partial ordering of weak mutually un-biased bases. In it, we studied a partial ordered relation which exists between a subsystem ^(q) and a larger system ^(d) and also, between a subgeometry Gq and larger geometry Gd. Furthermore, we show an isomorphism between: (i) the set {Gd} of subgeometries of a finite geometry Gd and subsets of the set {D(d)} of divisors of d. (ii) the set {hd} of subspaces of a finite Hilbert space Hd and subsets of the set {D(d)} of divisors of d. (iii) the set {Y(d)} of subsystems of a finite quantum system ^(d) and subsets of the set {D(d)} of divisors of d. We conclude this work by showing a duality between lines in finite geometry Gd and weak mutually unbiased bases in finite dimensional Hilbert space Hd.
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Partial ordering of weak mutually unbiased bases in finite quantum systemsOladejo, Semiu Oladipupo January 2015 (has links)
There has being an enormous work on finite quantum systems with variables in Zd, especially on mutually unbiased bases. The reason for this is due to its
wide areas of application. We focus on partial ordering of weak mutually un-biased bases. In it, we studied a partial ordered relation which exists between a subsystem ^(q) and a larger system ^(d) and also, between a subgeometry Gq and larger geometry Gd. Furthermore, we show an isomorphism between:
(i) the set {Gd} of subgeometries of a finite geometry Gd and subsets of the set {D(d)} of divisors of d.
(ii) the set {hd} of subspaces of a finite Hilbert space Hd and subsets of the set {D(d)} of divisors of d.
(iii) the set {Y(d)} of subsystems of a finite quantum system ^(d) and subsets of the set {D(d)} of divisors of d.
We conclude this work by showing a duality between lines in finite geometry Gd and weak mutually unbiased bases in finite dimensional Hilbert space Hd.
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Partial ordering of weak mutually unbiased basesOladejo, S.O., Lei, Ci, Vourdas, Apostolos 16 October 2014 (has links)
Yes / A quantum system (n) with variables in Z(n), where n = Qpi (with pi prime numbers), is
considered. The non-near-linear geometry G(n) of the phase space Z(n) × Z(n), is studied. The
lines through the origin are factorized in terms of ‘prime factor lines’ in Z(pi)×Z(pi). Weak mutually
unbiased bases (WMUB) which are products of the mutually unbiased bases in the ‘prime factor
Hilbert spaces’ H(pi), are also considered. The factorization of both lines and WMUB is analogous
to the factorization of integers in terms of prime numbers. The duality between lines and WMUB is
discussed. It is shown that there is a partial order in the set of subgeometries of G(n), isomorphic
to the partial order in the set of subsystems of (n).
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An analytic representation of weak mutually unbiased basesOlupitan, Tominiyi E. January 2016 (has links)
Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.
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An analytic representation of weak mutually unbiased basesOlupitan, Tominiyi E. January 2016 (has links)
Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.
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O arco associado a uma generalização da curva Hermitiana / The arc arising from a generalization of the Hermitian curveRibeiro, Beatriz Casulari da Motta, 1984- 12 June 2011 (has links)
Orientadores: Fernando Eduardo Torres Orihuela, Herivelto Martins Borges Filho / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T05:54:38Z (GMT). No. of bitstreams: 1
Ribeiro_BeatrizCasularidaMotta_D.pdf: 51476410 bytes, checksum: 46cb0c7a6206a5f0683b23a73ff3938e (MD5)
Previous issue date: 2011 / Resumo: Obtemos novos arcos completos associados ao conjunto de pontos racionais de uma certa generalização da curva Hermitiana que é Frobenius não-clássica. A construção está relacionada ao cálculo do número de pontos racionais de uma classe de curvas de Artin-Schreier / Abstract: We obtain new complete arcs arising from the set of rational points of a certain generalization of the Hermitian plane curve which is Frobenius non-classical. Our construction is related to the computation of the number of rational points of a class of Artin-Schreier curves / Doutorado / Matematica / Doutor em Matemática
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Quantum stabilizer codes and beyondSarvepalli, Pradeep Kiran 10 October 2008 (has links)
The importance of quantum error correction in paving the way to build a practical
quantum computer is no longer in doubt. Despite the large body of literature in quantum
coding theory, many important questions, especially those centering on the issue of "good
codes" are unresolved. In this dissertation the dominant underlying theme is that of constructing
good quantum codes. It approaches this problem from three rather different but
not exclusive strategies. Broadly, its contribution to the theory of quantum error correction
is threefold.
Firstly, it extends the framework of an important class of quantum codes - nonbinary
stabilizer codes. It clarifies the connections of stabilizer codes to classical codes over
quadratic extension fields, provides many new constructions of quantum codes, and develops
further the theory of optimal quantum codes and punctured quantum codes. In particular
it provides many explicit constructions of stabilizer codes, most notably it simplifies
the criteria by which quantum BCH codes can be constructed from classical codes.
Secondly, it contributes to the theory of operator quantum error correcting codes also
called as subsystem codes. These codes are expected to have efficient error recovery
schemes than stabilizer codes. Prior to our work however, systematic methods to construct
these codes were few and it was not clear how to fairly compare them with other classes of
quantum codes. This dissertation develops a framework for study and analysis of subsystem
codes using character theoretic methods. In particular, this work established a close
link between subsystem codes and classical codes and it became clear that the subsystem codes can be constructed from arbitrary classical codes.
Thirdly, it seeks to exploit the knowledge of noise to design efficient quantum codes
and considers more realistic channels than the commonly studied depolarizing channel.
It gives systematic constructions of asymmetric quantum stabilizer codes that exploit the
asymmetry of errors in certain quantum channels. This approach is based on a Calderbank-
Shor-Steane construction that combines BCH and finite geometry LDPC codes.
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