Results on Common Left/Right Divisors of Skew Polynomials

Since being introduced by Oystein Ore in his 1933 paper, “Theory of Non-Commutative Polynomials” [6], non-commutative, skew, or Ore polynomials have been studied extensively. One prominent application of skew polynomials is in the generation of codes. This paper covers some key facets of the structure of skew polynomials and aims to find a divisor polynomial for two given polynomials that satisfies certain properties of divisibility

Codes and Sequences for Information Retrieval and Stream Ciphers

Given a self-similar structure in codes and de Bruijn sequences, recursive techniques may be used to analyze and construct them. Batch codes partition the indices of code words into m buckets, where recovery of t symbols is accomplished by accessing at most tau in each bucket. This finds use in the retrieval of information spread over several devices. We introduce the concept of optimal batch codes, showing that binary Hamming codes and first order Reed-Muller codes are optimal. Then we study batch properties of binary Reed-Muller codes which have order less than half their length. Cartesian codes are defined by the evaluation of polynomials at a subset of points in F_q. We partition F_q into buckets defined by the quotient with a subspace V. Several properties equivalent to (V intersect ) = {0} for all i,j between 1 and mu are explored. With this framework, a code in F_q^(mu-1) capable of reconstructing mu indices is expanded to one in F_q^(mu) capable of reconstructing mu+1 indices. Using a base case in F_q^3, we are able to prove batch properties for codes in F_q. We generalize this to Cartesian Codes with a limit on the degree mu of the polynomials. De Bruijn sequences are cyclic sequences of length q^n that contain every q-ary word of length n exactly once. The pseudorandom properties of such sequences make them useful for stream ciphers. Under a particular homomorphism, the preimages of a binary de Bruijn sequence form two cycles. We examine a method for identifying points where these sequences may be joined to make a de Bruijn sequence of order n. Using the recursive structure of this construction, we are able to calculate sums of subsequences in O(n^4 log(n)) time, and the location of a word in O(n^5 log(n)) time. Together, these functions allow us to check the validity of any potential toggle point, which provides a method for efficiently generating a recursive specification. Each successful step takes O(k^5 log(k)), for k from 3 to n

On the anomalous afterglow seen in a chameleon afterglow search

We present data from our investigation of the anomalous orange-colored afterglow that was seen in the GammeV Chameleon Afterglow Search (CHASE). These data includes information about the broad band color of the observed glow, the relationship between the glow and the temperature of the apparatus, and other data taken prior to and during the science operations of CHASE. While differing in several details, the generic properties of the afterglow from CHASE are similar to luminescence seen in some vacuum compounds. Contamination from this, or similar, luminescent signatures will likely impact the design of implementation of future experiments involving single photon detectors and high intensity light sources in a cryogenic environment.Comment: 6 pages, 5 figures, submitted to PR

Batch Codes from Hamming and Reed-Muller Codes

Batch codes, introduced by Ishai \textit{et al.}, encode a string $x \in \Sigma^{k}$ into an $m$-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of $t$-users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. We look at locality and availability properties of first order Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than half their length

Search for axion-like particles using a variable baseline photon regeneration technique

We report the first results of the GammeV experiment, a search for milli-eV mass particles with axion-like couplings to two photons. The search is performed using a "light shining through a wall" technique where incident photons oscillate into new weakly interacting particles that are able to pass through the wall and subsequently regenerate back into detectable photons. The oscillation baseline of the apparatus is variable, thus allowing probes of different values of particle mass. We find no excess of events above background and are able to constrain the two-photon couplings of possible new scalar (pseudoscalar) particles to be less than 3.1x10^{-7} GeV^{-1} (3.5x10^{-7} GeV^{-1}) in the limit of massless particles.Comment: 5 pages, 4 figures. This is the version accepted by PRL and includes updated limit

A search for chameleon particles using a photon regeneration technique

We report the first results from the GammeV search for chameleon particles, which may be created via photon-photon interactions within a strong magnetic field. Chameleons are hypothesized scalar fields that could explain the dark energy problem. We implement a novel technique to create and trap the reflective particles within a jar and to detect them later via their afterglow as they slowly convert back into photons. These measurements provide the first experimental constraints on the couplings of chameleons to photons.Comment: 4 pages, 3 figures, accepted to PRL, minor revisions to introduction and a more quantitative estimate of reflection conditio

HyperCP: A high-rate spectrometer for the study of charged hyperon and kaon decays

The HyperCP experiment (Fermilab E871) was designed to search for rare phenomena in the decays of charged strange particles, in particular CP violation in $\Xi$ and $\Lambda$ hyperon decays with a sensitivity of $10^{-4}$. Intense charged secondary beams were produced by 800 GeV/c protons and momentum-selected by a magnetic channel. Decay products were detected in a large-acceptance, high-rate magnetic spectrometer using multiwire proportional chambers, trigger hodoscopes, a hadronic calorimeter, and a muon-detection system. Nearly identical acceptances and efficiencies for hyperons and antihyperons decaying within an evacuated volume were achieved by reversing the polarities of the channel and spectrometer magnets. A high-rate data-acquisition system enabled 231 billion events to be recorded in twelve months of data-taking.Comment: 107 pages, 45 Postscript figures, 14 tables, Elsevier LaTeX, submitted to Nucl. Instrum. Meth.