Matrix product and quasi-twisted codes in one class

Many classical constructions, such as Plotkin's and Turyn's, were generalized by matrix product (MP) codes. Quasi-twisted (QT) codes, on the other hand, form an algebraically rich structure class that contains many codes with best-known parameters. We significantly extend the definition of MP codes to establish a broader class of generalized matrix product (GMP) codes that contains QT codes as well. We propose a generator matrix formula for any linear GMP code and provide a condition for determining the code size. We prove that any QT code has a GMP structure. Then we show how to build a generator polynomial matrix for a QT code from its GMP structure, and vice versa. Despite that the class of QT codes contains many codes with best-known parameters, we present different examples of GMP codes with best-known parameters that are neither MP nor QT. Two different lower bounds on the minimum distance of GMP codes are presented; they generalize their counterparts in the MP codes literature. The second proposed lower bound replaces the non-singular by columns matrix with a less restrictive condition. Some examples are provided for comparing the two proposed bounds, as well as showing that these bounds are tight

Generator polynomial matrices of the Galois hulls of multi-twisted codes

In this study, we consider the Euclidean and Galois hulls of multi-twisted (MT) codes over a finite field $\mathbb{F}_{p^e}$ of characteristic $p$. Let $\mathbf{G}$ be a generator polynomial matrix (GPM) of a MT code $\mathcal{C}$. For any $0\le \kappa<e$, the $\kappa$-Galois hull of $\mathcal{C}$, denoted by $h_\kappa\left(\mathcal{C}\right)$, is the intersection of $\mathcal{C}$ with its $\kappa$-Galois dual. The main result in this paper is that a GPM for $h_\kappa\left(\mathcal{C}\right)$ has been obtained from $\mathbf{G}$. We start by associating a linear code $\mathcal{Q}_\mathbf{G}$ with $\mathbf{G}$. We show that $\mathcal{Q}_\mathbf{G}$ is quasi-cyclic. In addition, we prove that the dimension of $h_\kappa\left(\mathcal{C}\right)$ is the difference between the dimension of $\mathcal{C}$ and that of $\mathcal{Q}_\mathbf{G}$. Thus the determinantal divisors are used to derive a formula for the dimension of $h_\kappa\left(\mathcal{C}\right)$. Finally, we deduce a GPM formula for $h_\kappa\left(\mathcal{C}\right)$. In particular, we handle the cases of $\kappa$-Galois self-orthogonal and linear complementary dual MT codes; we establish equivalent conditions that characterize these cases. Equivalent results can be deduced immediately for the classes of cyclic, constacyclic, quasi-cyclic, generalized quasi-cyclic, and quasi-twisted codes, because they are all special cases of MT codes. Some numerical examples, containing optimal and maximum distance separable codes, are used to illustrate the theoretical results

Burnout among surgeons before and during the SARS-CoV-2 pandemic: an international survey

Background: SARS-CoV-2 pandemic has had many significant impacts within the surgical realm, and surgeons have been obligated to reconsider almost every aspect of daily clinical practice. Methods: This is a cross-sectional study reported in compliance with the CHERRIES guidelines and conducted through an online platform from June 14th to July 15th, 2020. The primary outcome was the burden of burnout during the pandemic indicated by the validated Shirom-Melamed Burnout Measure. Results: Nine hundred fifty-four surgeons completed the survey. The median length of practice was 10&nbsp;years; 78.2% included were male with a median age of 37&nbsp;years old, 39.5% were consultants, 68.9% were general surgeons, and 55.7% were affiliated with an academic institution. Overall, there was a significant increase in the mean burnout score during the pandemic; longer years of practice and older age were significantly associated with less burnout. There were significant reductions in the median number of outpatient visits, operated cases, on-call hours, emergency visits, and research work, so, 48.2% of respondents felt that the training resources were insufficient. The majority (81.3%) of respondents reported that their hospitals were included in the management of COVID-19, 66.5% felt their roles had been minimized; 41% were asked to assist in non-surgical medical practices, and 37.6% of respondents were included in COVID-19 management. Conclusions: There was a significant burnout among trainees. Almost all aspects of clinical and research activities were affected with a significant reduction in the volume of research, outpatient clinic visits, surgical procedures, on-call hours, and emergency cases hindering the training. Trial registration: The study was registered on clicaltrials.gov "NCT04433286" on 16/06/2020

Optimized Polar Codes as Forward Error Correction Coding for Digital Video Broadcasting Systems

Polar codes are featured by their low encoding/decoding complexity for symmetric binary input-discrete memoryless channels. Recently, flexible generic Successive Cancellation List (SCL) decoders for polar codes were proposed to provide different throughput, latency, and decoding performances. In this paper, we propose to use polar codes with flexible fast-adaptive SCL decoders in Digital Video Broadcasting (DVB) systems to meet the growing demand for more bitrates. In addition, they can provide more interactive services with less latency and more throughput. First, we start with the construction of polar codes and propose a new mathematical relation to get the optimized design point for the polar code. We prove that our optimized design point is too close to the one that achieves minimum Bit Error Rate (BER). Then, we compare the performance of polar and Low-Density Parity Check (LDPC) codes in terms of BER, encoder/decoder latencies, and throughput. The results show that both channel coding techniques have comparable BER. However, polar codes are superior to LDPC in terms of decoding latency, and system throughput. Finally, we present the possible performance enhancement of DVB systems in terms of decoding latency and complexity when using optimized polar codes as a Forward Error Correction (FEC) technique instead of Bose Chaudhuri Hocquenghem (BCH) and LDPC codes that are currently adopted in DVB standards