Two-weight and three-weight linear codes constructed from Weil sums

<p style='text-indent:20px;'>Linear codes with few weights are widely used in strongly regular graphs, secret sharing schemes, association schemes and authentication codes. In this paper, we construct several two-weight and three-weight linear codes over finite fields by choosing suitable different defining sets. We also give some examples and some of the codes are optimal or almost optimal. Their applications to secret sharing schemes are also investigated.</p>

The Talmudic Logic Project, Ongoing Since 2008

We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools. We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. http://www.collegepublications.co.uk/stl/ The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are two fold:To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed.To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic.

Identifying Mixed Mycobacterium tuberculosis Infection and Laboratory Cross-Contamination during Mycobacterial Sequencing Programs

ABSTRACT The detection of laboratory cross-contamination and mixed tuberculosis infections is an important goal of clinical mycobacteriology laboratories. The objective of this study was to develop a method to detect mixtures of different Mycobacterium tuberculosis lineages in laboratories performing mycobacterial next-generation sequencing (NGS). The setting was the Public Health England National Mycobacteriology Laboratory Birmingham, which performs Illumina sequencing on DNA extracted from positive mycobacterial growth indicator tubes. We analyzed 4,156 samples yielding M. tuberculosis from 663 MiSeq runs, which were obtained during development and production use of a diagnostic process using NGS. The counts of the most common (major) variant and all other variants (nonmajor variants) were determined from reads mapping to positions defining M. tuberculosis lineages. Expected variation was estimated during process development. For each sample, we determined the nonmajor variant proportions at 55 sets of lineage-defining positions. The nonmajor variant proportion in the two most mixed lineage-defining sets (F2 metric) was compared with that of the 47 least-mixed lineage-defining sets (F47 metric). The following three patterns were observed: (i) not mixed by either metric; (ii) high F47 metric, suggesting mixtures of multiple lineages; and (iii) samples compatible with mixtures of two lineages, detected by differential F2 metric elevations relative to F47. Pattern ii was observed in batches, with similar patterns in the M. tuberculosis H37Rv control present in each run, and is likely to reflect cross-contamination. During production, the proportions of samples in the patterns were 97%, 2.8%, and 0.001%, respectively. The F2 and F47 metrics described could be used for laboratory process control in laboratories sequencing M. tuberculosis genomes.

Identifying mixed Mycobacterium tuberculosis infection and laboratory cross-contamination during Mycobacterial sequencing programs

ABSTRACTIntroductionDetecting laboratory cross-contamination and mixed tuberculosis infection are important goals of clinical Mycobacteriology laboratories.ObjectivesTo develop a method detecting mixtures of different M. tuberculosis lineages in laboratories performing Mycobacterial next generation sequencing (NGS).SettingPublic Health England National Mycobacteriology Laboratory Birmingham, which performs Illumina sequencing on DNA extracted from positive Mycobacterial Growth Indicator tubes.MethodsWe analysed 4,156 samples yielding M. tuberculosis from 663 MiSeq runs, obtained during development and production use of a diagnostic process using NGS. Counts of the most common (major) variant, and all other variants (non-major variants) were determined from reads mapping to positions defining M. tuberculosis lineages. Expected variation was estimated during process development.ResultsFor each sample we determined the non-major variant proportions at 55 sets of lineage defining positions. The non-major variant proportion in the two most mixed lineage defining sets (F2 metric) was compared with that in the 47 least mixed lineage defining sets (F47 metric). Three patterns were observed: (i) not mixed by either metric, (ii) high F47 metric suggesting mixtures of multiple lineages, and (iii) samples compatible with mixtures of two lineages, detected by differential F2 metric elevation relative to F47. Pattern (ii) was observed in batches, with similar patterns in the H37Rv control present in each run, and is likely to reflect cross-contamination. During production, the proportions of samples in each pattern were 97%, 2.8%, and 0.001%, respectively.ConclusionThe F2 and F47 metrics described could be used for laboratory process control in laboratories sequencing M. tuberculosis.

FEW-WEIGHT CODES FROM TRACE CODES OVER

We construct two families of few-weight codes for the Lee weight over the ring $R_{k}$ based on two different defining sets. For the first defining set, taking the Gray map, we obtain an infinite family of binary two-weight codes which are in fact $2^{k}$-fold replicated MacDonald codes. For the second defining set, we obtain two infinite families of few-weight codes. These few-weight codes can be used to implement secret-sharing schemes.