The dual of convolutional codes over Zpr\mathbb{Z}_{p^r}

An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to con- volutional codes over finite fields. The extension of the concept of convolutional codes from finite fields to finite rings have attracted much attention in recent years due to fact that they are the most appropriate codes for phase modulation. However convolutional codes over finite rings are more involved and not fully understood. Many results and features that are well-known for convolutional codes over finite fields have not been fully investigated in the context of finite rings. In this paper we focus in one of these unexplored areas, namely, we investigate the dual codes of convolutional codes over finite rings. In particular we study the p-dimension of the dual code of a convolutional code over a finite ring. This contribution can be considered a generalization and an extension, to the rings case, of the work done by Forney and McEliece on the dimension of the dual code of a convolutional code over a finite field.Comment: submitte

LIFTED CODES OVER FINITE CHAIN RINGS

In this paper, we study lifted codes over finite chain rings. We use γ-adic codes over a formal power series ring to study codes over finite chain rings

Lifted codes and their weight enumerators

AbstractWe describe some structural results for codes over the rings Zp and use them to examine lifts of codes over these rings to Zpe and to codes over the p-adics. We determine the weight enumerator of all lifts of the length 8 Hamming code and the length 12 ternary Golay code. We show that all weight enumerators of the lifts of the length 24 Golay code can be determined after a finite computation

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The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual codes over Galois rings GF (2e, l) of length n = 2l for any a ≥ 1 and l ≥ 2. Torsion codes over residue fields of finite chain rings are introduced, and some of their properties are derived. Finally, we describe MDS codes and self-dual codes over finite principal ideal rings by examining codes over their component chain rings, via a generalized Chinese remainder theorem

MDS and Self-dual Codes over Rings

In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings

Adaptive Filter Solution For Processing Lidar Returns: Optical Parameter Estimation

Joint estimation of extinction and backscatter simulated profiles from elastic-backscatter lidar return signals is tackled by means of an extended Kalman filter (EKF). First, we introduced the issue from a theoretical point of view by using both an EKF formulation and an appropriate atmospheric stochastic model; second, it is tested through extensive simulation and under simplified conditions; and, finally, a first real application is discussed. An atmospheric model including both temporal and spatial correlation features is introduced to describe approximate fluctuation statistics in the sought-after atmospheric optical parameters and hence to include a priori information in the algorithm. Provided that reasonable models are given for the filter, inversion errors are shown to depend strongly on the atmospheric condition (i.e., the visibility) and the signal-to-noise ratio along the exploration path in spite of modeling errors in the assumed statistical properties of the atmospheric optical parameters. This is of advantage in the performance of the Kalman filter because they are often the point of most concern in identification problems. In light of the adaptive behavior of the filter and the inversion results, the EKF approach promises a successful alternative to present-day nonmemory algorithms based on exponential-curve fitting or differential equation formulations such as Klett’s method.Peer Reviewe

Horizontal plasmid transfer among klebsiella pneumoniae isolates is the key factor for dissemination of extended-spectrum β-lactamases among children in Tanzania

Increased knowledge about the role of horizontal gene transfer is key to improve our understanding of the spread of antimicrobial resistance (AMR) in human populations. We therefore studied the dissemination of the blaCTX-M-15 extended-spectrum-β-lactamase (ESBL) gene in Klebsiella pneumoniae isolates obtained from stool samples from hospitalized children and healthy controls below 2 years of age in Dar es Salaam, Tanzania, from August 2010 to July 2011. We performed Illumina whole-genome sequencing (WGS) to characterize resistance genes, multilocus sequence type (MLST), plasmid incompatibility group (Inc), and plasmid MLST of 128 isolates of K. pneumoniae with blaCTX-M-15 recovered from both healthy and hospitalized children. We assessed the phylogenetic relationship using single nucleotide polymorphism (SNP)-based analysis and resolved the sequences of five reference plasmids by Oxford Nanopore technology to investigate plasmid dissemination. The WGS analyses revealed the presence of a blaCTX-M-15-positive IncFIIK5/IncR plasmid with a highly conserved backbone in 70% (90/128) of the isolates. This plasmid, harboring genes encoding resistance to most β-lactams, aminoglycosides, trimethoprim-sulfamethoxazole, and chloramphenicol, was present in phylogenetically very diverse K. pneumoniae strains (48 different MLSTs) carried by both hospitalized and healthy children. Our data strongly suggest widespread horizontal transfer of this ESBL-carrying plasmid both in hospitals and in the general population. IMPORTANCE - Horizontal spread of plasmids carrying multiple resistance genes is considered an important mechanism behind the global health problem caused by multidrug-resistant bacteria. Nevertheless, knowledge about spread of plasmids in a community is limited. Our detailed molecular analyses of K. pneumoniae isolated from hospitalized and healthy children in Tanzania disclosed an epidemic spread of a resistance plasmid. In this study population, we revealed horizontal plasmid transfer among K. pneumoniae as the key factor for dissemination of ESBLs. Traditional outbreak investigation and surveillance focus on the spread of bacterial clones, and short-read sequencing can result in erroneous plasmid composition. Our approach using long-read sequencing reveals horizontal gene transfer of antimicrobial resistance, and therefore has a potential impact on outbreak investigations and approaches to limit spread of AMR