Optimal locally repairable codes of distance 33 and 44 via cyclic codes

Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code {\it optimal} if it achieves the Singleton-type bound). In the breakthrough work of \cite{TB14}, several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in \cite{TB14} are upper bounded by the code alphabet size $q$. Recently, it was proved through extension of construction in \cite{TB14} that length of $q$-ary optimal locally repairable codes can be $q+1$ in \cite{JMX17}. Surprisingly, \cite{BHHMV16} presented a few examples of $q$-ary optimal locally repairable codes of small distance and locality with code length achieving roughly $q^2$. Very recently, it was further shown in \cite{LMX17} that there exist $q$-ary optimal locally repairable codes with length bigger than $q+1$ and distance propositional to $n$. Thus, it becomes an interesting and challenging problem to construct new families of $q$-ary optimal locally repairable codes of length bigger than $q+1$. In this paper, we construct a class of optimal locally repairable codes of distance $3$ and $4$ with unbounded length (i.e., length of the codes is independent of the code alphabet size). Our technique is through cyclic codes with particular generator and parity-check polynomials that are carefully chosen

The Research on Exogenous Problems of Farmers’ Piritual and Cultural Education in China

The author studied and analyzed the exogenous problems of the farmers’ spiritual and cultural education, and found out: In today’s China, the exogenous problems of the farmers’ spiritual and cultural education mainly reflected in the separation of spiritual and cultural education is from social environment, political system, economic development, and cultural concepts etc. Then the author put forward to the countermeasures and suggestions aimed at optimizing the allocation of famers’ spiritual and cultural educations resources, environment and evaluation system construction and so on

Prognosis for patients with apical hypertrophic cardiomyopathy: A multicenter cohort study based on propensity score matching

Background: Apical hypertrophic cardiomyopathy (AHCM) is a subtype of HCM, and few studies on the prognosis in AHCM are available.Aims: This study aimed to explore the clinical prognosis for AHCM and non-AHCM patients through clinical data based on propensity score matching (PSM) in a large cohort of Chinese HCM patients.Methods: The cohort study included 2268 HCM patients, 226 AHCM and 2042 non-AHCM patients from 13 tertiary hospitals, who were treated between 1996 and 2021. Fifteen demographic and clinical variables of 226 AHCM patients and 2042 non-AHCM patients were matched using 1:2 PSM. A Cox proportional hazard regression model was constructed to assess the effect of AHCM on mortality.Results: During a median follow-up of 5.1 (2.4–8.4) years, 353 (15.6%) of the 2268 HCM patients died, of whom 205 died due to cardiovascular mortality/cardiac transplantation and 94 experienced sudden cardiac death (SCD). In the matched cohort, the ACHM patients had lower rates of all-cause mortality (P = 0.003), cardiovascular mortality/cardiac transplantation (P = 0.03), and SCD (P = 0.02) than the non-AHCM patients. Furthermore, the Cox proportional hazard regression model showed that AHCM was an independent prognostic predictor of all-cause HCM mortality (P = 0.004) and a univariable prognostic predictor of cardiovascular mortality/cardiac transplantation (P = 0.03) and for SCD (P = 0.03). However, AHCM was not significant in multivariable Cox regression models in relation to cardiovascular mortality/cardiac transplantation and SCD.Conclusion: AHCM had a favorable prognosis both before and after matching, with lower all-cause mortality, cardiovascular mortality/cardiac transplantation, and SCD than non-AHCM

Generalization of Steane’s enlargement construction of quantum codes and applications

We generalize Steane’s enlargement construction of binary quantum codes to q-ary quantum codes. We then apply this result to BCH codes and the study of asymptotic bounds, and obtain improvements to the quantum BCH codes constructed by Aly and Klappenecker and the quantum asymptotic bounds from algebraic geometry codes obtained by Feng, Ling and Xing.Accepted versio