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We study codes with parameters of $q$ -ary shortened Hamming codes, i.e., $(n=(q^{m}-q)/(q-1), q^{n-m}, 3)_{q}$. Firstly, we prove the fact mentioned in 1998 by Brouwer et al. that such codes are optimal, generalizing it to a bound for multifold packings of radius-1 balls, with a corollary for multiple coverings. In particular, we show that the punctured Hamming code is an optimal $q$ -fold packing with minimum distance 2. Secondly, for every admissible length starting from $n=20$ , we show the existence of 4-ary codes with parameters of shortened 1-perfect codes that cannot be obtained by shortening a 1-perfect code. [ABSTRACT FROM AUTHOR]

We investigate fat projective linear codes over ${\mathbb Z}_{p^{m}}$ , $m\geqslant 2$ , with two nonzero homogeneous weights (“two-weight codes”), building on the graph theory approach developed by Delsarte for codes over fields. Our main result is the classification of such codes under the additional assumption that the columns of a generator matrix of the code determine a cap in the projective Hjelmslev geometry $\mathop {\mathrm {PHG}}\nolimits (k-1, {\mathbb Z}_{p^{m}})$. This generalizes a result on projective two weight codes with dual distance at least four (Calderbank, 1982). The proof relies on a careful analysis of a certain strongly regular graph built on the cosets of the dual code, and on an interpretation of its parameters in terms of projective Hjelmslev geometry. [ABSTRACT FROM AUTHOR]

We study the k-Galois linear complementary dual (LCD) codes over the finite chain ring R = Fq + uFq with u2 = 0, where q = pe and p is a prime number. We give a sufficient condition on the generator matrix for the existence of k-Galois LCD codes over R. Finally, we show that a linear code over R (for k = 0, q > 3) is equivalent to a Euclidean LCD code, and a linear code over R (for 0, (pe−k + 1) (pe−1) and (pe−1)/(pe−k + 1) > 1) is equivalent to a k-Galois LCD code. [ABSTRACT FROM AUTHOR]

We study the k-Galois linear complementary dual (LCD) codes over the finite chain ring R = Fq + uFq with u2 = 0, where q = pe and p is a prime number. We give a sufficient condition on the generator matrix for the existence of k-Galois LCD codes over R. Finally, we show that a linear code over R (for k = 0, q > 3) is equivalent to a Euclidean LCD code, and a linear code over R (for 0, (pe−k + 1) (pe−1) and (pe−1)/(pe−k + 1) > 1) is equivalent to a k-Galois LCD code. [ABSTRACT FROM AUTHOR]

Mixed alphabet codes are the generalizations of the classical linear codes over finite fields and rings. In this letter we introduce a valid method of constructing FpR-additive codes, where p is a prime number, and R = Fp + uFp with u2 = 0. These codes can be viewed as a combination of irreducible cyclic codes over Fp and trace codes over R. In particular, by using the Gray map, part of the obtained image codes meets the Greismer bound with equality, and can be applied to construct new secret sharing scheme. [ABSTRACT FROM AUTHOR]

We use the Weather Research and Forecasting Model with the chemistry/Data Assimilation Research Testbed (WRF‐Chem/DART) chemical weather forecasting/data assimilation system with multiconstituent data assimilation to investigate the improvement of air quality forecasts over eastern China. We assimilate surface in situ observations of sulfur dioxide (SO2), nitrogen dioxide (NO2), ozone (O3), carbon monoxide (CO), particulate matter with diameters less than 2.5 μm (PM2.5) and 10 μm (PM10), and satellite aerosol optical depth to adjust the related anthropogenic emissions as well as the chemical initial conditions. We validate our forecast results out to 72 hr by comparison with the in situ observations. Results show that updated emissions improve the model performance between 10% and 65% root mean square error reduction for the assimilated species except particulate matter with a diameter between 2.5 and 10 μm (PM2.5‐10), which is slightly improved due to the limited anthropogenic contribution to it. In a sensitivity experiment with a different update interval, the CO improvement is found to be sensitive to the cycling time used to update the CO emissions. In another sensitivity experiment when NO2 observations are not assimilated and nitrogen oxides (NOx) emission are adjusted by only O3, NO2 forecasts show similar root mean square error improvement but have lower spatial correlation, indicating the value and limitation of the O3‐NOx cross‐variable relationship. Key Points: We assimilated multiconstituent observations to adjust the related anthropogenic emissions over the eastern part of ChinaEmissions updated by data assimilation could yield generally better model performance in forecasting species assimilatedTime interval used to update the CO emissions is important; joint assimilation of both ozone and nitrogen dioxide is also necessary [ABSTRACT FROM AUTHOR]

In this paper, two different Gray-like maps from $Z_{p}^\alpha \times Z_{p^{k}}^\beta $ , where $p$ is prime, to $Z_{p}^{n}$ , $n={\alpha +\beta p^{k-1}}$ , denoted by $\varphi $ and $\Phi $ , respectively, are presented. We have determined the connection between the weight enumerators among the image codes under these two mappings. We show that if $C$ is a $Z_{p} Z_{p^{k}}$ -additive code, and $C^\bot $ is its dual, then the weight enumerators of the image $p$ -ary codes $\varphi (C)$ and $\Phi (C^\bot)$ are formally dual. This is a partial generalization of [D. S. Krotov, On $Z_{2^{k}}$ -dual binary codes, IEEE Transactions Information Theory 53 (2007), 1532–1537], and the result is generalized to odd characteristic $p$ and mixed alphabet. In addition, a construction of 1-perfect additive codes in the mixed $Z_{p} Z_{p^{2}}\ldots Z_{p^{k}}$ alphabet is given. [ABSTRACT FROM AUTHOR]

Quasi-twisted codes of fixed index >1 have been shown recently to be asymptotically good (A. Alahmadi, C. Güneri, H. Shoaib, P. Solé, 2017). We use this result to construct asymptotically good additive constacyclic codes on any extension of a fixed degree of the base field. A similar result is proved for additive cyclic codes under Artin conjecture on primitive roots. [ABSTRACT FROM AUTHOR]

We construct an infinite family of three-Lee-weight codes of dimension 2 m, where m is singly-even, over the ring $\mathbb {F}_{p}+u\mathbb {F}_{p}$ with u =0. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain an infinite family of abelian p-ary three-weight codes. When m is odd, and p≡3 (mod 4), we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. An application to secret sharing schemes is given. [ABSTRACT FROM AUTHOR]

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM). Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number RO is not very large and the drag coefficient CD is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as RO or CD increases. [ABSTRACT FROM AUTHOR]

In this work, we study a family of self-dual four circulant codes and a family of self-dual four negacirculant codes, and the exact counting formula is derived for these families of codes. In addition, we prove that asymptotically good self-dual four circulant codes and negacirculant codes over finite fields exist, and both of them satisfy a modified Gilbert-Varshamov bound on the relative minimum distance with asymptotic rate 1 2. [ABSTRACT FROM AUTHOR]

Three types of observations, aerosol optical depth from the Moderate Resolution Imaging Spectroradiometer, surface particulate matter with diameters less than 2.5 (PM2.5) and 10 μm (PM10), and aerosol extinction coefficient (AEXT) profiles from ground‐based lidars, were separately and simultaneously assimilated using the Weather Research and Forecasting Model with the Chemistry/Data Assimilation Research Testbed (WRF‐Chem/DART). Two cases in June and November 2018 were selected over middle and eastern China. Experiments assimilating single‐type and multiple observations were evaluated by cross validating their analysis and forecast against the three observation types. Compared to the experiment without data assimilation (DA), DA of single‐type observations is always closer to the type of observations assimilated. However, DA of aerosol optical depth or AEXT sometimes significantly degraded the error performance for PM2.5. This problem is caused by the inconsistency of bias tendencies when modeling aerosol optical properties and surface aerosol mass. It is found that WRF‐Chem tends to predict dryer air within the boundary layer over eastern China, which may have played a role in the underestimation of AEXT even when PM2.5 was overestimated. After applying a simple bias correction (BC), the problem was alleviated. DA of multiple observations with BC gives the best overall error performance when validated against all types of observations and even performs better than any DA of single‐type observations experiments in reproducing AEXT profiles. The results illustrate that BC is important in DA of multiple observations and that the simultaneous DA of aerosol observations with different vertical information can work synergistically to improve aerosol forecasts. Key Points: Multiple aerosol data from satellite, surface site, and ground‐based lidar were assimilated, which improved model's overall performanceBias correction is crucial in data assimilation of multiple observations if bias tendencies are different in different observation typesA new bias correction method for ensemble Kalman filter was proposed and tested [ABSTRACT FROM AUTHOR]

γ-interferon-inducible protein-16 (IFI16), a key DNA sensor, triggers downstream STING-dependent type I interferon (IFN-I) production and antiviral immunity. However, it is still unclear how to negatively regulate IFI16 to avoid excessive IFN-I production and autoimmunity. Here, we find that STING directly interacts with IFI16 and facilitates IFI16 degradation via the ubiquitin-proteasome pathway by recruiting the E3 ligase TRIM21. The 1-pyrin region of IFI16 is responsible for the IFI16-STING interaction, and the first three lysines in the N-terminal region of IFI16 are the key sites that lead to STING-mediated IFI16 ubiquitination and degradation. Compared to wild-type IFI16, a higher level of viral DNA triggered IFN-β and antiviral IFN-stimulated gene expression, and thus less HSV-1 infection, was observed in the cells transfected with IFI16-K3/4/6R, an IFI16 mutant that is resistant to degradation. STING-mediated negative feedback regulation of IFI16 restricts IFN-I overproduction during antiviral immunity to avoid autoimmune diseases. • Overexpression of STING facilitates IFI16 degradation • E3 ligase TRIM21 plays a role in STING-mediated IFI16 degradation • IFI16-K3/4/6R mutation stabilizes IFI16 protein • IFI16-K3/4/6R facilitates type I IFN production Li et al. show that STING mediates negative feedback regulation of IFI16 and restricts type I IFN overproduction during immune responses to viruses such as HSV-1. [ABSTRACT FROM AUTHOR]