Results for "Paul M. Geil"
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List decoding of a class of affine variety codesJan 26 2011Consider a polynomial $F$ in $m$ variables and a finite point ensemble $S=S_1 \times ... \times S_m$. When given the leading monomial of $F$ with respect to a lexicographic ordering we derive improved information on the possible number of zeros of $F$ ... More Weighted Reed-Muller codes revisitedAug 31 2011We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio $|S_1|/|S_2|$ on the ... More More results on the number of zeros of multiplicity at least rOct 26 2014Dec 22 2015We consider multivariate polynomials and investigate how many zeros of multiplicity at least $r$ they can have over a Cartesian product of finite subsets of a field. Here r is any prescribed positive integer and the definition of multiplicity that we ... More Relative generalized Hamming weights of q-ary Reed-Muller codesJul 23 2014Nov 03 2015Coset constructions of $q$-ary Reed-Muller codes can be used to store secrets on a distributed storage system in such a way that only parties with access to a large part of the system can obtain information while still allowing for local error-correction. ... More On affine variety codes from the Klein quarticJun 18 2017We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in [12, Ex. 3.2]. Among the codes that we construct almost all have parameters as good as the best known codes according ... More Further improvements on the Feng-Rao bound for dual codesMay 06 2013Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement ... More On the number of zeros of multiplicity rDec 08 2009Dec 21 2009Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and ... More An improvement of the Feng-Rao bound for primary codesJul 11 2013Jul 24 2013We present a new bound for the minimum distance of a general primary linear code. For affine variety codes defined from generalised C_{ab} curves the new bound often improves dramatically on the Feng-Rao bound for primary codes. The method does not only ... More On nested code pairs from the Hermitian curveJul 11 2018Jul 18 2018Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [16] and in the CSS construction of quantum codes [15]. The important parameters are (1) the codimension, (2) the relative minimum distance of the codes, and (3) ... More Steane-Enlargement of Quantum Codes from the Hermitian CurveApr 22 2019In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, ... More A Note on the Injection DistanceDec 09 2009Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs asymptotically optimal ... More 2H-NMR studies of supercooled and glassy aspirinJan 10 2007Acetyl salicylic acid, deuterated at the methyl group, was investigated using 2H-NMR in its supercooled and glassy states. Just above the glass transition temperature the molecular reorientations were studied using stimulated-echo spectroscopy and demonstrated ... More Feng-Rao decoding of primary codesOct 25 2012Oct 31 2012We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil [H.E. Andersen and O. Geil, Evaluation codes from order domain theory, Finite Fields Appl., 14 (2008), pp. 92-123] for primary codes are consequences of each other. ... More On Field Size and Success Probability in Network CodingJun 27 2008Using tools from algebraic geometry and Groebner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the ... More RegistersDec 05 2006Entry in: Encyclopedia of Algorithms, Ming-Yang Kao, Ed., Springer, To appear. Synonyms: Wait-free registers, wait-free shared variables, asynchronous communication hardware. Problem Definition: Consider a system of asynchronous processes that communicate ... More RandomnessOct 08 2001Oct 10 2001Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its Applications" ... More Conditional Kolmogorov Complexity and Universal ProbabilityJun 05 2012Jan 22 2013The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. There are conditional versions referred to in several publications but as yet there exist no written proofs in English. Here ... More Information Distance in MultiplesMay 20 2009Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples (finite lists). ... More On Empirical EntropyMar 30 2011We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the description of the random ... More How big are the smallest drops of quark-gluon plasma?Jan 07 2016Feb 22 2016Using holographic duality, we present results for both head-on and off-center collisions of Gaussian shock waves in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory. The shock waves superficially resemble Lorentz contracted colliding ... More Oscillon Lifetime in the Presence of Quantum FluctuationsJan 23 2014Jul 23 2014We consider the stability of oscillons in 2+1 space-time dimensions, in the presence of quantum fluctuations. Taking the oscillon to be the inhomogeneous mean field of a self-interacting quantum scalar field, we compare its classical evolution to the ... More Compression-based SimilarityOct 20 2011First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned, normalized, and ... More Colliding shock waves and hydrodynamics in small systemsJun 07 2015Dec 15 2015Using numerical holography, we study the collision of a planar sheet of energy with a bounded localized distribution of energy. The collision, which mimics proton-nucleus collisions, produces a localized lump of debris with transverse size $R \sim 1/T_{\rm ... More A New Approximation to the Normal Distribution Quantile FunctionFeb 02 2010Feb 03 2010We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2.5 \cdot 10^{-5}$. This is less accurate than [3], but ... More Trading leads to scale-free self-organizationMay 29 2009Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of ... More Recrudescence of massive fermion production by oscillonsDec 06 2016In this letter we bring together the physics of preheating, following a period of inflation, and the dynamics of non-topological solitons, namely oscillons. We show that the oscillating condensate that makes up an oscillon can be an efficient engine for ... More Distributed elections in an Archimedean ring of processorsMay 27 2009Unlimited asynchronism is intolerable in real physically distributed computer systems. Such systems, synchronous or not, use clocks and timeouts. Therefore the magnitudes of elapsed absolute time in the system need to satisfy the axiom of Archimedes. ... More Primitive divisors of Lucas and Lehmer sequencesJan 31 2012Stewart reduced the problem of determining all Lucas and Lehmer sequences whose $n$-th element does not have a primitive divisor to solving certain Thue equations. Using the method of Tzanakis and de Weger for solving Thue equations, we determine such ... More On The Average-Case Complexity of ShellsortJan 26 2015Jan 27 2015We prove a lower bound expressed in the increment sequence on the average-case complexity (number of inversions which is proportional to the running time) of Shellsort. This lower bound is sharp in every case where it could be checked. We obtain new results ... More Quantum Kolmogorov Complexity Based on Classical DescriptionsFeb 21 2001Oct 09 2001We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity coincides with ... More Carbon isotope measurements in the Solar SystemJan 28 2009Feb 02 2010I make publicly available my literature study into carbon isotope ratios in the Solar System, which formed a part of Woods & Willacy (2009). As far as I know, I have included here all measurements of 12C/13C in Solar System objects (excluding those of ... More Lattice effects on nematic quantum criticality in metalsOct 19 2016Metals near a nematic quantum critical point, where systems are poised to undergo a zero temperature continuous phase transition that breaks rotational symmetry, are of great interest for studying the iron superconductors, cuprates, ruthanates, and quantum ... More The Candy-Passing Game for c\geq3n-2Sep 13 2007Nov 25 2007We determine the behavior of Tanton's candy-passing game for all distributions of at least 3n-2 candies, where n is the number of students. Specifically, we show that the configuration of candy in such a game eventually becomes fixed.