Z2Z4-additive codes

Altres ajuts: UAB PNL2006-13The Combinatoric, Coding and Security Group (CCSG) is a research group in the Department of Information and Communications Engineering (DEIC) at the Universitat Aut'onoma de Barcelona (UAB). The research group CCSG has been uninterruptedly working since 1987 in several projects and research activities on Information Theory, Communications, Coding Theory, Source Coding, Cryptography, Electronic Voting, Network Coding, etc. The members of the group have been producing mainly results on optimal coding. Specifically, the research has been focused on uniformly-packed codes; perfect codes in the Hamming space; perfect codes in distance-regular graphs; the classification of optimal codes of a given length; and codes which are close to optimal codes by some properties, for example, Reed-Muller codes, Preparata codes, Kerdock codes and Hadamard codes. Part of the research developed by CCSG deals with Z2Z4-linear codes. There are no symbolic software to work with these codes, so the members of CCSG have been developing this new package that supports the basic facilities for Z2Z4-additive codes. Specifically, this Magma package generalizes most of the known functions for codes over the ring Z4, which are subgroups of Zn4, to Z2Z4-additive codes, which are subgroups of Zγ2 × Zδ4, maintaining all the functionality for codes over Z4 and adding new functions which, not only generalize the previous ones, but introduce new variants when it is needed. A beta version of this new package for Z2Z4-additive codes and this manual with the description of all functions can be downloaded from the web page http://ccsg.uab.cat. For any comment or further information about this package, you can send an e-mail to [email protected]. The authors would like to thank Lorena Ronquillo, Jaume Pernas, Roger Ten-Valls, and Cristina Diéguez for their contributions developing some parts of this Magma package

Z2Z4-additive codes

Altres ajuts: UAB PNL2006-13The Combinatoric, Coding and Security Group (CCSG) is a research group in the Department of Information and Communications Engineering (DEIC) at the Universitat Aut'onoma de Barcelona (UAB). The research group CCSG has been uninterruptedly working since 1987 in several projects and research activities on Information Theory, Communications, Coding Theory, Source Coding, Cryptography, Electronic Voting, Network Coding, etc. The members of the group have been producing mainly results on optimal coding. Specifically, the research has been focused on uniformly-packed codes; perfect codes in the Hamming space; perfect codes in distance-regular graphs; the classification of optimal codes of a given length; and codes which are close to optimal codes by some properties, for example, Reed-Muller codes, Preparata codes, Kerdock codes and Hadamard codes. Part of the research developed by CCSG deals with Z2Z4-linear codes. There are no symbolic software to work with these codes, so the members of CCSG have been developing this new package that supports the basic facilities for Z2Z4-additive codes. Specifically, this Magma package generalizes most of the known functions for codes over the ring Z4, which are subgroups of Zn4, to Z2Z4-additive codes, which are subgroups of Zγ2 × Zδ4, maintaining all the functionality for codes over Z4 and adding new functions which, not only generalize the previous ones, but introduce new variants when it is needed. A beta version of this new package for Z2Z4-additive codes and this manual with the description of all functions can be downloaded from the web page http://ccsg.uab.cat. For any comment or further information about this package, you can send an e-mail to [email protected]. The authors would like to thank Lorena Ronquillo, Jaume Pernas, Roger Ten-Valls, and Cristina Diéguez for their contributions developing some parts of this Magma package

Profiling post-COVID-19 condition across different variants of SARS-CoV-2: a prospective longitudinal study in unvaccinated wild-type, unvaccinated alpha-variant, and vaccinated delta-variant populations

BACKGROUND: Self-reported symptom studies rapidly increased understanding of SARS-CoV-2 during the COVID-19 pandemic and enabled monitoring of long-term effects of COVID-19 outside hospital settings. Post-COVID-19 condition presents as heterogeneous profiles, which need characterisation to enable personalised patient care. We aimed to describe post-COVID-19 condition profiles by viral variant and vaccination status. METHODS: In this prospective longitudinal cohort study, we analysed data from UK-based adults (aged 18–100 years) who regularly provided health reports via the Covid Symptom Study smartphone app between March 24, 2020, and Dec 8, 2021. We included participants who reported feeling physically normal for at least 30 days before testing positive for SARS-CoV-2 who subsequently developed long COVID (ie, symptoms lasting longer than 28 days from the date of the initial positive test). We separately defined post-COVID-19 condition as symptoms that persisted for at least 84 days after the initial positive test. We did unsupervised clustering analysis of time-series data to identify distinct symptom profiles for vaccinated and unvaccinated people with post-COVID-19 condition after infection with the wild-type, alpha (B.1.1.7), or delta (B.1.617.2 and AY.x) variants of SARS-CoV-2. Clusters were then characterised on the basis of symptom prevalence, duration, demography, and previous comorbidities. We also used an additional testing sample with additional data from the Covid Symptom Study Biobank (collected between October, 2020, and April, 2021) to investigate the effects of the identified symptom clusters of post-COVID-19 condition on the lives of affected people. FINDINGS: We included 9804 people from the COVID Symptom Study with long COVID, 1513 (15%) of whom developed post-COVID-19 condition. Sample sizes were sufficient only for analyses of the unvaccinated wild-type, unvaccinated alpha variant, and vaccinated delta variant groups. We identified distinct profiles of symptoms for post-COVID-19 condition within and across variants: four endotypes were identified for infections due to the wild-type variant (in unvaccinated people), seven for the alpha variant (in unvaccinated people), and five for the delta variant (in vaccinated people). Across all variants, we identified a cardiorespiratory cluster of symptoms, a central neurological cluster, and a multi-organ systemic inflammatory cluster. These three main clusers were confirmed in a testing sample. Gastrointestinal symptoms clustered in no more than two specific phenotypes per viral variant. INTERPRETATION: Our unsupervised analysis identified different profiles of post-COVID-19 condition, characterised by differing symptom combinations, durations, and functional outcomes. Our classification could be useful for understanding the distinct mechanisms of post-COVID-19 condition, as well as for identification of subgroups of individuals who might be at risk of prolonged debilitation. FUNDING: UK Government Department of Health and Social Care, Chronic Disease Research Foundation, The Wellcome Trust, UK Engineering and Physical Sciences Research Council, UK Research and Innovation London Medical Imaging & Artificial Intelligence Centre for Value-Based Healthcare, UK National Institute for Health Research, UK Medical Research Council, British Heart Foundation, UK Alzheimer's Society, and ZOE

Detecting COVID-19 infection hotspots in England using large-scale self-reported data from a mobile application: a prospective, observational study

BACKGROUND: As many countries seek to slow the spread of COVID-19 without reimposing national restrictions, it has become important to track the disease at a local level to identify areas in need of targeted intervention. METHODS: In this prospective, observational study, we did modelling using longitudinal, self-reported data from users of the COVID Symptom Study app in England between March 24, and Sept 29, 2020. Beginning on April 28, in England, the Department of Health and Social Care allocated RT-PCR tests for COVID-19 to app users who logged themselves as healthy at least once in 9 days and then reported any symptom. We calculated incidence of COVID-19 using the invited swab (RT-PCR) tests reported in the app, and we estimated prevalence using a symptom-based method (using logistic regression) and a method based on both symptoms and swab test results. We used incidence rates to estimate the effective reproduction number, R(t), modelling the system as a Poisson process and using Markov Chain Monte-Carlo. We used three datasets to validate our models: the Office for National Statistics (ONS) Community Infection Survey, the Real-time Assessment of Community Transmission (REACT-1) study, and UK Government testing data. We used geographically granular estimates to highlight regions with rapidly increasing case numbers, or hotspots. FINDINGS: From March 24 to Sept 29, 2020, a total of 2 873 726 users living in England signed up to use the app, of whom 2 842 732 (98·9%) provided valid age information and daily assessments. These users provided a total of 120 192 306 daily reports of their symptoms, and recorded the results of 169 682 invited swab tests. On a national level, our estimates of incidence and prevalence showed a similar sensitivity to changes to those reported in the ONS and REACT-1 studies. On Sept 28, 2020, we estimated an incidence of 15 841 (95% CI 14 023-17 885) daily cases, a prevalence of 0·53% (0·45-0·60), and R(t) of 1·17 (1·15-1·19) in England. On a geographically granular level, on Sept 28, 2020, we detected 15 (75%) of the 20 regions with highest incidence according to government test data. INTERPRETATION: Our method could help to detect rapid case increases in regions where government testing provision is lower. Self-reported data from mobile applications can provide an agile resource to inform policy makers during a quickly moving pandemic, serving as a complementary resource to more traditional instruments for disease surveillance. FUNDING: Zoe Global, UK Government Department of Health and Social Care, Wellcome Trust, UK Engineering and Physical Sciences Research Council, UK National Institute for Health Research, UK Medical Research Council and British Heart Foundation, Alzheimer's Society, Chronic Disease Research Foundation

Estrogen and COVID-19 symptoms: Associations in women from the COVID Symptom Study

It has been widely observed that adult men of all ages are at higher risk of developing serious complications from COVID-19 when compared with women. This study aimed to investigate the association of COVID-19 positivity and severity with estrogen exposure in women, in a population based matched cohort study of female users of the COVID Symptom Study application in the UK. Analyses included 152,637 women for menopausal status, 295,689 women for exogenous estrogen intake in the form of the combined oral contraceptive pill (COCP), and 151,193 menopausal women for hormone replacement therapy (HRT). Data were collected using the COVID Symptom Study in May-June 2020. Analyses investigated associations between predicted or tested COVID-19 status and menopausal status, COCP use, and HRT use, adjusting for age, smoking and BMI, with follow-up age sensitivity analysis, and validation in a subset of participants from the TwinsUK cohort. Menopausal women had higher rates of predicted COVID-19 (P = 0.003). COCP-users had lower rates of predicted COVID-19 (P = 8.03E-05), with reduction in hospital attendance (P = 0.023). Menopausal women using HRT or hormonal therapies did not exhibit consistent associations, including increased rates of predicted COVID-19 (P = 2.22E-05) for HRT users alone. The findings support a protective effect of estrogen exposure on COVID-19, based on positive association between predicted COVID-19 with menopausal status, and negative association with COCP use. HRT use was positively associated with COVID-19, but the results should be considered with caution due to lack of data on HRT type, route of administration, duration of treatment, and potential unaccounted for confounders and comorbidities

Illness duration and symptom profile in symptomatic UK school-aged children tested for SARS-CoV-2.

BACKGROUND: In children, SARS-CoV-2 infection is usually asymptomatic or causes a mild illness of short duration. Persistent illness has been reported; however, its prevalence and characteristics are unclear. We aimed to determine illness duration and characteristics in symptomatic UK school-aged children tested for SARS-CoV-2 using data from the COVID Symptom Study, one of the largest UK citizen participatory epidemiological studies to date. METHODS: In this prospective cohort study, data from UK school-aged children (age 5-17 years) were reported by an adult proxy. Participants were voluntary, and used a mobile application (app) launched jointly by Zoe Limited and King's College London. Illness duration and symptom prevalence, duration, and burden were analysed for children testing positive for SARS-CoV-2 for whom illness duration could be determined, and were assessed overall and for younger (age 5-11 years) and older (age 12-17 years) groups. Children with longer than 1 week between symptomatic reports on the app were excluded from analysis. Data from symptomatic children testing negative for SARS-CoV-2, matched 1:1 for age, gender, and week of testing, were also assessed. FINDINGS: 258 790 children aged 5-17 years were reported by an adult proxy between March 24, 2020, and Feb 22, 2021, of whom 75 529 had valid test results for SARS-CoV-2. 1734 children (588 younger and 1146 older children) had a positive SARS-CoV-2 test result and calculable illness duration within the study timeframe (illness onset between Sept 1, 2020, and Jan 24, 2021). The most common symptoms were headache (1079 [62·2%] of 1734 children), and fatigue (954 [55·0%] of 1734 children). Median illness duration was 6 days (IQR 3-11) versus 3 days (2-7) in children testing negative, and was positively associated with age (Spearman's rank-order rs 0·19, p<0·0001). Median illness duration was longer for older children (7 days, IQR 3-12) than younger children (5 days, 2-9). 77 (4·4%) of 1734 children had illness duration of at least 28 days, more commonly in older than younger children (59 [5·1%] of 1146 older children vs 18 [3·1%] of 588 younger children; p=0·046). The commonest symptoms experienced by these children during the first 4 weeks of illness were fatigue (65 [84·4%] of 77), headache (60 [77·9%] of 77), and anosmia (60 [77·9%] of 77); however, after day 28 the symptom burden was low (median 2 symptoms, IQR 1-4) compared with the first week of illness (median 6 symptoms, 4-8). Only 25 (1·8%) of 1379 children experienced symptoms for at least 56 days. Few children (15 children, 0·9%) in the negatively tested cohort had symptoms for at least 28 days; however, these children experienced greater symptom burden throughout their illness (9 symptoms, IQR 7·7-11·0 vs 8, 6-9) and after day 28 (5 symptoms, IQR 1·5-6·5 vs 2, 1-4) than did children who tested positive for SARS-CoV-2. INTERPRETATION: Although COVID-19 in children is usually of short duration with low symptom burden, some children with COVID-19 experience prolonged illness duration. Reassuringly, symptom burden in these children did not increase with time, and most recovered by day 56. Some children who tested negative for SARS-CoV-2 also had persistent and burdensome illness. A holistic approach for all children with persistent illness during the pandemic is appropriate. FUNDING: Zoe Limited, UK Government Department of Health and Social Care, Wellcome Trust, UK Engineering and Physical Sciences Research Council, UK Research and Innovation London Medical Imaging and Artificial Intelligence Centre for Value Based Healthcare, UK National Institute for Health Research, UK Medical Research Council, British Heart Foundation, and Alzheimer's Society

Illness Characteristics of COVID-19 in Children Infected with the SARS-CoV-2 Delta Variant.

BACKGROUND: The Delta (B.1.617.2) SARS-CoV-2 variant was the predominant UK circulating strain between May and November 2021. We investigated whether COVID-19 from Delta infection differed from infection with previous variants in children. METHODS: Through the prospective COVID Symptom Study, 109,626 UK school-aged children were proxy-reported between 28 December 2020 and 8 July 2021. We selected all symptomatic children who tested positive for SARS-CoV-2 and were proxy-reported at least weekly, within two timeframes: 28 December 2020 to 6 May 2021 (Alpha (B.1.1.7), the main UK circulating variant) and 26 May to 8 July 2021 (Delta, the main UK circulating variant), with all children unvaccinated (as per national policy at the time). We assessed illness profiles (symptom prevalence, duration, and burden), hospital presentation, and presence of long (≥28 day) illness, and calculated odds ratios for symptoms presenting within the first 28 days of illness. RESULTS: 694 (276 younger (5-11 years), 418 older (12-17 years)) symptomatic children tested positive for SARS-CoV-2 with Alpha infection and 706 (227 younger and 479 older) children with Delta infection. Median illness duration was short with either variant (overall cohort: 5 days (IQR 2-9.75) with Alpha, 5 days (IQR 2-9) with Delta). The seven most prevalent symptoms were common to both variants. Symptom burden over the first 28 days was slightly greater with Delta compared with Alpha infection (in younger children, 3 (IQR 2-5) symptoms with Alpha, 4 (IQR 2-7) with Delta; in older children, 5 (IQR 3-8) symptoms with Alpha, 6 (IQR 3-9) with Delta infection ). The odds of presenting several symptoms were higher with Delta than Alpha infection, including headache and fever. Few children presented to hospital, and long illness duration was uncommon, with either variant. CONCLUSIONS: COVID-19 in UK school-aged children due to SARS-CoV-2 Delta strain B.1.617.2 resembles illness due to the Alpha variant B.1.1.7., with short duration and similar symptom burden

Recobriment i grafs distància-regulars

Uno de los aspectos claves en las telecomunicaciones está relacionado con el uso de los códigos correctores de errores para la transmisión de información. Actualmente se utiliza una clase muy simple de códigos; la implementación física de un código corrector de errores es complicada y costosa. En el campo de la Informática Teórica se intenta abordar el problema de los códigos correctores de errores desde diferentes ángulos. Uno de ellos es el de la Combinatoria Algebraica y, en particular, los grafos distancia-regulares, con los cuales podemos contruir buenos códigos. En [10] se prueba que partiendo de un grafo distancia-regular Γ, e-reticular (e ≥ 3), de valencia n, podemos construir, para cada vértice α Î ≥, una aplicación θα: (Z/2)n → Γ, que es un "recubrimiento", tal que el conjunto C = θα-1(α) es un código completamente regular. En [7], K. Nomura generaliza este resultado para el caso no binario. Las construcciones del código anterior y del recubrimiento θ se basan en propiedades locales del grafo Γ, es decir, no es necesario utilizar las características globales del grafo distancia-regular. En este artículo presentamos las líneas más importantes de la teoría básica de los grafos distancia-regulares necesarias para construir el recubrimiento θα: (Z/2)n → Γ. También construimos este recubrimiento y generalizamos el resultado de [10] en el sentido de clarificar que θ también es un e-recubrimiento, e ≥ 3. Este último resultado es la clave en el estudio de las propiedades algebraicas de los códigos completamente regulares asociados a los grafos distancia-regulares [11]

Survey on Z₂Z₄-additive codes

A code C is Z₂Z₄-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y ) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of Z₂Z₄-additive codes under an extended Gray map are called Z₂Z₄-linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are shown and standard forms for generator and parity-check matrices are given, defining the appropriate concept of duality. The main results on Z₂Z₄-additive self-dual and Z₂Z₄-additive formally self-dual codes are also presented, as well as, the results on the invariants rank and dimension of the kernel for these codes are given. Several families of important binary codes fall in the class of Z₂Z₄-linear codes. In this survey, we review characterizations, properties and constructions of perfect and extended perfect Z₂Z₄-linear codes, Hadamard Z₂Z₄-linear codes, Reed-Muller Z₂Z₄-linear codes, maximum distance separable Z₂Z₄-linear codes, and Preparata-like and Kerdock-like Z₂Z₄-linear codes. Finally, applications of Z₂Z₄-additive codes to steganography are also presented