scholarly journals Group matrix ring codes and constructions of self-dual codes

2021 ◽  
Author(s):  
S. T. Dougherty ◽  
Adrian Korban ◽  
Serap Şahinkaya ◽  
Deniz Ustun
Keyword(s):  
Matrix Ring ◽  
Type I ◽  
Type Ii ◽  
Dual Codes ◽  
Generator Matrix ◽  
Matrix Rings ◽  
Group Matrix ◽  
The Matrix ◽  
New Type ◽  
Matrix Construction

AbstractIn this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring $$M_k(R)$$ M k ( R ) and the ring R,  where R is the commutative Frobenius ring. We show that codes over the ring $$M_k(R)$$ M k ( R ) are one sided ideals in the group matrix ring $$M_k(R)G$$ M k ( R ) G and the corresponding codes over the ring R are $$G^k$$ G k -codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes.

scholarly journals Isodual and self-dual codes from graphs

2021 ◽  
Vol 32 (1) ◽  
pp. 49-64
Author(s):  
S. Mallik ◽  
◽  
B. Yildiz ◽  
Keyword(s):  
Minimum Distance ◽  
Linear Codes ◽  
Type I ◽  
Type Ii ◽  
Dual Codes ◽  
Generator Matrix ◽  
Combinatorial Interpretation ◽  
Binary Linear Codes ◽  
Graph Theoretic ◽  
Graph Classes

Binary linear codes are constructed from graphs, in particular, by the generator matrix [In|A] where A is the adjacency matrix of a graph on n vertices. A combinatorial interpretation of the minimum distance of such codes is given. We also present graph theoretic conditions for such linear codes to be Type I and Type II self-dual. Several examples of binary linear codes produced by well-known graph classes are given.

Type I and Type II codes over the ring 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2

2019 ◽  
Vol 12 (02) ◽  
pp. 1950025 ◽  
Author(s):  
Ankur ◽  
Pramod Kumar Kewat
Keyword(s):  
Type I ◽  
Type Ii ◽  
Dual Codes ◽  
Generator Matrix ◽  
Type Ii Codes

We discuss self-dual codes over the ring [Formula: see text]. We characterize the structure of self-dual, Type I codes and Type II codes over [Formula: see text] with given generator matrix in terms of the structure of their Torsion and Residue codes. We construct self-dual, Type I and Type II codes over [Formula: see text] for different lengths.

scholarly journals Complementation of the Jacobson group in a matrix ring

2005 ◽  
Vol 72 (2) ◽  
pp. 317-324
Author(s):  
David Dolžan
Keyword(s):  
Normal Subgroup ◽  
Commutative Ring ◽  
Jacobson Radical ◽  
Matrix Ring ◽  
Graded Rings ◽  
Matrix Rings ◽  
Generators And Relations ◽  
Group Of Units ◽  
The Matrix ◽  
Finite Commutative Ring

The Jacobson group of a ring R (denoted by  = (R)) is the normal subgroup of the group of units of R (denoted by G(R)) obtained by adding 1 to the Jacobson radical of R (J(R)). Coleman and Easdown in 2000 showed that the Jacobson group is complemented in the group of units of any finite commutative ring and also in the group of units a n × n matrix ring over integers modulo ps, when n = 2 and p = 2, 3, but it is not complemented when p ≥ 5. In 2004 Wilcox showed that the answer is positive also for n = 3 and p = 2, and negative in all the remaining cases. In this paper we offer a different proof for Wilcox's results and also generalise the results to a matrix ring over an arbitrary finite commutative ring. We show this by studying the generators and relations that define a matrix ring over a field. We then proceed to examine the complementation of the Jacobson group in the matrix rings over graded rings and prove that complementation depends only on the 0-th grade.

scholarly journals Cellular heterogeneity in cultured human chondrocytes identified by antibodies specific for alpha 2(XI) collagen chains.

1989 ◽  
Vol 109 (3) ◽  
pp. 1363-1369 ◽  
Author(s):  
B Swoboda ◽  
R Holmdahl ◽  
H Stöss ◽  
K von der Mark
Keyword(s):  
Hyaline Cartilage ◽  
Type Ii Collagen ◽  
Cross Reactivity ◽  
Cellular Heterogeneity ◽  
Human Chondrocytes ◽  
Type I ◽  
Type Ii ◽  
Human Cartilage ◽  
The Matrix ◽  
Type Xi Collagen

Collagen type XI is a component of hyaline cartilage consisting of alpha 1(XI), alpha 2(XI), and alpha 3(XI) chains; with 5-10% of the total collagen content, it is a minor but significant component next to type II collagen, but its function and precise localization in cartilaginous tissues is still unclear. Owing to the homology of the alpha 3(XI) and alpha 1(II) collagen chains, attempts to prepare specific antibodies to native type XI collagen have been unsuccessful in the past. In this study, we report on the preparation and use for immunohistochemistry of a polyclonal antibody specific for alpha 2(XI) denatured collagen chains. The antibody was prepared by immunization with the isolated alpha 2(XI) chain and reacts neither with native type XI collagen nor type I, II, V, or IX by ELISA or immunoblotting, nor with alpha 1(XI) or alpha 3(XI), but with alpha 2(XI) chains. Using this antibody, it was possible to specifically localize alpha 2(XI) in cartilage by pretreating tissue sections with 6 M urea. In double immunofluorescence staining experiments, the distribution of alpha 2(XI) as indicative for type XI collagen in fetal bovine and human cartilage was compared with that of type II collagen, using a monoclonal antibody to alpha 1(II). Type XI collagen was found throughout the matrix of hyaline cartilage. However, owing to cross-reactivity of the monoclonal anti-alpha 1(II) with alpha 3(XI), both antibodies produced the same staining pattern. Cellular heterogeneity was, however, detected in monolayer cultures of human chondrocytes.(ABSTRACT TRUNCATED AT 250 WORDS)

The Type I/Type II Perceptual Dichotomy: A Reanalysis for the Illusions of Extent

1987 ◽  
Vol 65 (3) ◽  
pp. 751-754 ◽  
Author(s):  
Ted Jaeger
Keyword(s):  
Type I ◽  
Type Ii ◽  
Geometrical Illusions ◽  
New Type ◽  
Age Trends

The categorization of geometrical illusions of extent as Type I or Type II phenomena based on variation in magnitude with age is critically examined. Methodological shortcomings and the failure of contemporary findings to show matching age trends for components of a single illusion are presented as factors undermining the usefulness of this perceptual dichotomy. Finally, it is shown that a new Type I/Type II dichotomy based on changes in perceived size rather than amount of illusion indicates a developmental commonality among most of the illusions of extent.

Combined HRTEM and EFTEM Study of Precipitates in Tungsten and Chromium-Containing TiB2

1999 ◽  
Vol 589 ◽  
Author(s):  
W. Mader ◽  
B. Freitag ◽  
K. Kelm ◽  
R. Telle ◽  
C. Schmalzried
Keyword(s):  
Chemical Composition ◽  
Structural Model ◽  
Chemical Constituents ◽  
Type I ◽  
Type Ii ◽  
Resolution Limit ◽  
Energy Filtering ◽  
The Matrix ◽  
Tungsten Concentration ◽  
Elemental Maps

AbstractThe structure and chemical composition of two types of precipitates in the system TiB2-WB2-CrB2 were studied by means of high-resolution TEM and energy filtering TEM. Type I particles (W2B5 structure) are precipitated at the basal plane of the hexagonal matrix whereas type II precipitates are thin platelets lying parallel to the {1100} prism planes. Lattice imaging yields displacements of the metal positions with respect to the matrix. Information on the chemical composition at high lateral resolution is obtained from elemental maps of all chemical constituents using electron spectroscopic imaging (ESI). The type II precipitates show a decrease in the B and Ti concentration, whereas the tungsten concentration increases and the Cr is homogeneously distributed. The HRTEM results combined with the results of the elemental maps allow to develop a structural model based on the intergrowth of the β-WB structure in the TiB2-rich matrix. The two deficient boron layers in W0.5Ti0.5B with a spacing of 0.38 nm can be used to examine the resolution limit of ESI.

Derivations of some classes of matrix rings

2017 ◽  
Vol 16 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Feride Kuzucuoğlu ◽  
Umut Sayın
Keyword(s):  
Associative Ring ◽  
Matrix Ring ◽  
Matrix Rings ◽  
Ideal Formula ◽  
The Matrix

Let [Formula: see text] be the ring of all (lower) niltriangular [Formula: see text] matrices over any associative ring [Formula: see text] with identity and [Formula: see text] be the ring of all [Formula: see text] matrices over an ideal [Formula: see text] of [Formula: see text]. We describe all derivations of the matrix ring [Formula: see text].

scholarly journals Solar Radio Emission of Spectral Type IV and its Association with Geomagnetic Storms

1959 ◽  
Vol 12 (4) ◽  
pp. 404 ◽  
Author(s):  
DJ McLean
Keyword(s):  
Solar Flares ◽  
Solar Radio ◽  
Geomagnetic Storms ◽  
Close Association ◽  
Solar Radio Emission ◽  
Type I ◽  
Type Ii ◽  
Type Iv ◽  
New Type ◽  
Radio Event

A new type of solar radio event, the type IV storm, first described by Boischot, has been identified on Dapto radio.spectrographic records. It has been shown to be distinguishable from type I storms by (i) its smooth spectrum, (ii) its close association with type II bursts, and (iii) its remarkably close association with geomagnetic storms. In common with some type I storms, all type IV storms are found to be associated with very large solar flares.

Study on the behaviour of DS-Class inclusions in advanced bearing steel

2019 ◽  
Vol 116 (2) ◽  
pp. 223
Author(s):  
Huajie Wu ◽  
Qiaoqi Li ◽  
Chongyi Wei ◽  
Zhe Wang
Keyword(s):  
Reaction Time ◽  
Bearing Steel ◽  
Refining Process ◽  
Formation Mechanisms ◽  
Type I ◽  
Type Ii ◽  
The Core ◽  
Metallic Inclusions ◽  
The Matrix ◽  
Solid Phases

The source and generated mechanisms of DS-size inclusions in bearing steel were studied by sampling systematically and using ASPEX, SEM and EDS to analyse the morphology, composition and amount of non-metallic inclusions larger than 13 µm. Two kinds of typical DS-size inclusions were found in the refining process: type I is CaO-MgO-Al2O3-SiO2 distributed evenly and wrapped by CaS; type II is composite inclusion with MgO-Al2O3 as the core, CaO-Al2O3 and CaO-SiO2 as the inner layer, covered by CaS. Based on the FactSage and thermodynamic calculations, the DS inclusions formation mechanisms were drawn. There are two formation mechanisms of the type II inclusions: one is the solid phases will precipitate from the matrix of type I inclusions as the temperature drops; another is that when the reaction time is not sufficient, the MgO∙Al2O3 spinel core will not be transformed completely, and the evolution can be summarized as: Al2O3 → MgO-Al2O3 → CaO-MgO-Al2O3 → surrounded by CaO-Al2O3(SiO2) → covered by CaS.

scholarly journals Interferon Lambda: A New Sword in Cancer Immunotherapy

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmed Lasfar ◽  
Walid Abushahba ◽  
Murugabaskar Balan ◽  
Karine A. Cohen-Solal
Keyword(s):  
Viral Infections ◽  
Type I ◽  
Type Ii ◽  
Type Iii ◽  
Group Type ◽  
Interferon Lambda ◽  
New Type ◽  
Cell Type Specific ◽  
Type Iii Ifn

The discovery of the interferon-lambda (IFN-λ) family has considerably contributed to our understanding of the role of interferon not only in viral infections but also in cancer. IFN-λproteins belong to the new type III IFN group. Type III IFN is structurally similar to type II IFN (IFN-γ) but functionally identical to type I IFN (IFN-α/β). However, in contrast to type I or type II IFNs, the response to type III IFN is highly cell-type specific. Only epithelial-like cells and to a lesser extent some immune cells respond to IFN-λ. This particular pattern of response is controlled by the differential expression of the IFN-λreceptor, which, in contrast to IFN-α, should result in limited side effects in patients. Recently, we and other groups have shown in several animal models a potent antitumor role of IFN-λthat will open a new challenging era for the current IFN therapy.

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