Fast syndrome-based Chase decoding of binary BCH codes through Wu list decoding

We present a new fast Chase decoding algorithm for binary BCH codes. The new algorithm reduces the complexity in comparison to a recent fast Chase decoding algorithm for Reed--Solomon (RS) codes by the authors (IEEE Trans. IT, 2022), by requiring only a single Koetter iteration per edge of the decoding tree. In comparison to the fast Chase algorithms presented by Kamiya (IEEE Trans. IT, 2001) and Wu (IEEE Trans. IT, 2012) for binary BCH codes, the polynomials updated throughout the algorithm of the current paper typically have a much lower degree. To achieve the complexity reduction, we build on a new isomorphism between two solution modules in the binary case, and on a degenerate case of the soft-decision (SD) version of the Wu list decoding algorithm. Roughly speaking, we prove that when the maximum list size is $1$ in Wu list decoding of binary BCH codes, assigning a multiplicity of $1$ to a coordinate has the same effect as flipping this coordinate in a Chase-decoding trial. The solution-module isomorphism also provides a systematic way to benefit from the binary alphabet for reducing the complexity in bounded-distance hard-decision (HD) decoding. Along the way, we briefly develop the Groebner-bases formulation of the Wu list decoding algorithm for binary BCH codes, which is missing in the literature

Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes

We present $O(m^3)$ algorithms for specifying the support of minimum-weight words of extended binary BCH codes of length $n=2^m$ and designed distance $d(m,s,i):=2^{m-1-s}-2^{m-1-i-s}$ for some values of $m,i,s$, where $m$ may grow to infinity. The support is specified as the sum of two sets: a set of $2^{2i-1}-2^{i-1}$ elements, and a subspace of dimension $m-2i-s$, specified by a basis. In some detail, for designed distance $6\cdot 2^j$, we have a deterministic algorithm for even $m\geq 4$, and a probabilistic algorithm with success probability $1-O(2^{-m})$ for odd $m>4$. For designed distance $28\cdot 2^j$, we have a probabilistic algorithm with success probability $\geq 1/3-O(2^{-m/2})$ for even $m\geq 6$. Finally, for designed distance $120\cdot 2^j$, we have a deterministic algorithm for $m\geq 8$ divisible by $4$. We also present a construction via Gold functions when $2i|m$. Our construction builds on results of Kasami and Lin (IEEE T-IT, 1972), who proved that for extended binary BCH codes of designed distance $d(m,s,i)$, the minimum distance equals the designed distance. Their proof makes use of a non-constructive result of Berlekamp (Inform. Contrl., 1970), and a constructive ``down-conversion theorem'' that converts some words in BCH codes to lower-weight words in BCH codes of lower designed distance. Our main contribution is in replacing the non-constructive argument of Berlekamp by a low-complexity algorithm. In one aspect, we extends the results of Grigorescu and Kaufman (IEEE T-IT, 2012), who presented explicit minimum-weight words for designed distance $6$ (and hence also for designed distance $6\cdot 2^j$, by a well-known ``up-conversion theorem''), as we cover more cases of the minimum distance. However, the minimum-weight words we construct are not affine generators for designed distance $>6$

Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals

We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.Comment: 18 pages, minor changes, references added. Version accepted by JHE

QlicRice: a web interface for abiotic stress responsive QTL and loci interaction channels in rice

The QlicRice database is designed to host publicly accessible, abiotic stress responsive quantitative trait loci (QTLs) in rice (Oryza sativa) and their corresponding sequenced gene loci. It provides a platform for the data mining of abiotic stress responsive QTLs, as well as browsing and annotating associated traits, their location on a sequenced genome, mapped expressed sequence tags (ESTs) and tissue and growth stage-specific expressions on the whole genome. Information on QTLs related to abiotic stresses and their corresponding loci from a genomic perspective has not yet been integrated on an accessible, user-friendly platform. QlicRice offers client-responsive architecture to retrieve meaningful biological information—integrated and named ‘Qlic Search’—embedded in a query phrase autocomplete feature, coupled with multiple search options that include trait names, genes and QTL IDs. A comprehensive physical and genetic map and vital statistics have been provided in a graphical manner for deciphering the position of QTLs on different chromosomes. A convenient and intuitive user interface have been designed to help users retrieve associations to agronomically important QTLs on abiotic stress response in rice

Motion frozen 18F-FDG cardiac PET

BackgroundPET reconstruction incorporating spatially variant 3D Point Spread Function (PSF) improves contrast and image resolution. "Cardiac Motion Frozen" (CMF) processing eliminates the influence of cardiac motion in static summed images. We have evaluated the combined use of CMF- and PSF-based reconstruction for high-resolution cardiac PET.MethodsStatic and 16-bin ECG-gated images of 20 patients referred for (18)F-FDG myocardial viability scans were obtained on a Siemens Biograph-64. CMF was applied to the gated images reconstructed with PSF. Myocardium to blood contrast, maximum left ventricle (LV) counts to defect contrast, contrast-to-noise (CNR) and wall thickness with standard reconstruction (2D-AWOSEM), PSF, ED-gated PSF, and CMF-PSF were compared.ResultsThe measured wall thickness was 18.9 ± 5.2 mm for 2D-AWOSEM, 16.6 ± 4.5 mm for PSF, and 13.8 ± 3.9 mm for CMF-PSF reconstructed images (all P < .05). The CMF-PSF myocardium to blood and maximum LV counts to defect contrasts (5.7 ± 2.7, 10.0 ± 5.7) were higher than for 2D-AWOSEM (3.5 ± 1.4, 6.5 ± 3.1) and for PSF (3.9 ± 1.7, 7.7 ± 3.7) (CMF vs all other, P < .05). The CNR for CMF-PSF (26.3 ± 17.5) was comparable to PSF (29.1 ± 18.3), but higher than for ED-gated dataset (13.7 ± 8.8, P < .05).ConclusionCombined CMF-PSF reconstruction increased myocardium to blood contrast, maximum LV counts to defect contrast and maintained equivalent noise when compared to static summed 2D-AWOSEM and PSF reconstruction

Intangible resources of competitive advantage: Analysis of 49 Asian airlines across three business models

Without sustainable competitive advantage firms have limited economic reasons to exist and will decline. Competitive advantage concerns the factors which provide competitive strength. This paper is based upon the resource-based view which considers firm resources to be heterogeneous and which believes that firms only have a small bundle of core resources irrespective of their overall performance. This research establishes the role of 36 intangible resources for 49 Asian airlines across three business models: network airlines; low-cost subsidiaries from network airlines; and low-cost carriers. It uses the VRIN framework which examines whether resources are valuable, rare, inimitable, and non-substitutable. Research participants distribute points between their chosen seven resources according to their perceived role in firm performance. Resources which meet all four requirements of VRIN are considered core competences and sources of sustained advantage. Across all 49 Asian airlines, the top-three most important resources of advantage are slots, brand, and product/service reputation. While these core resources are predictable, they have not previously been proven within the context of airlines, let alone geographically and by airline model. Results show that the core bundle of resources vary for each model, which helps to explain the difference in performance across models, and that some resources which were expected to be high-ranking, such as organisational culture and customer focus, were not.Full Tex

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure