Type I neighbors of extremal type II codes of length 40 derived from Hadamard matrices

Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over GF(2) and GF(4) with minimal shadow. In particular, we prove that there is no near-extremal Type I [24m,12m,2m+2] binary self-dual code with minimal shadow if m≥323, and we prove that there is no near-extremal Type I (6m+1,26m+1,2m+1) additive self-dual code over GF(4) with minimal shadow if m≥22.

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

Asian-European Journal of Mathematics ◽

10.1142/s1793557119500256 ◽

2019 ◽

Vol 12 (02) ◽

pp. 1950025 ◽

Cited By ~ 1

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.

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Byte weight enumerators and modular forms of genus r

Journal of Algebra and Its Applications ◽

10.1142/s0219498815500802 ◽

2015 ◽

Vol 14 (06) ◽

pp. 1550080

Author(s):

Anuradha Sharma ◽

Amit K. Sharma

Keyword(s):

Modular Forms ◽

Quadratic Forms ◽

Zeta Functions ◽

Siegel Modular Forms ◽

Type I ◽

Type Ii ◽

Jacobi Forms ◽

Weight Enumerators ◽

Type Ii Codes ◽

Real Quaternions

For a positive integer m, let R be either the ring ℤ2m of integers modulo 2m or the quaternionic ring Σ2m = ℤ2m + αℤ2m + βℤ2m + γℤ2m with α = 1 + î, β = 1 + ĵ and [Formula: see text], where [Formula: see text] are elements of the ring ℍ of real quaternions satisfying [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. In this paper, we obtain Jacobi forms (or Siegel modular forms) of genus r from byte weight enumerators (or symmetrized byte weight enumerators) in genus r of Type I and Type II codes over R. Furthermore, we derive a functional equation for partial Epstein zeta functions, which are summands of classical Epstein zeta functions associated with quadratic forms.

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Heat-Etching with a Bullivant Type II Simple Freeze-Cleave Device

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100067522 ◽

1970 ◽

Vol 28 ◽

pp. 106-107 ◽

Cited By ~ 1

Author(s):

Ronald S. Weinstein ◽

N. Scott McNutt

Keyword(s):

New Zealand ◽

General Hospital ◽

Massachusetts General Hospital ◽

Type I ◽

Type Ii ◽

Collaborative Effort ◽

Temperature And Pressure ◽

The University

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.

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Labelling of non-A, non-B hepatitis infected chimpanzee hepatocytes with nuclease-gold conjugates

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100111367 ◽

1984 ◽

Vol 42 ◽

pp. 250-251

Author(s):

G. D. Gagne ◽

M. F. Miller ◽

D. A. Peterson

Keyword(s):

Endoplasmic Reticulum ◽

Experimental Infection ◽

Uranyl Acetate ◽

Type I ◽

Cellular Injury ◽

Type Ii ◽

Tubular Structures ◽

Type Iii ◽

Type Iv ◽

Infected Chimpanzee

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.

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Comparative surface and ultrastructural views of methylotrophic bacteria by TEM, STEM, SE, and freeze-etch electron microscopy.

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100128274 ◽

1987 ◽

Vol 45 ◽

pp. 792-793

Author(s):

T.A. Fassel ◽

M.J. Schaller ◽

M.E. Lidstrom ◽

C.C. Remsen

Keyword(s):

Cytoplasmic Membrane ◽

Structural Features ◽

Methylotrophic Bacteria ◽

Type I ◽

Type Ii ◽

Membrane Complex ◽

Oxidation Of Methane ◽

Methane Oxidizing Bacteria ◽

Wall Structures ◽

Methylomonas Albus

Methylotrophic bacteria play an Important role in the environment in the oxidation of methane and methanol. Extensive intracytoplasmic membranes (ICM) have been associated with the oxidation processes in methylotrophs and chemolithotrophic bacteria. Classification on the basis of ICM arrangement distinguishes 2 types of methylotrophs. Bundles or vesicular stacks of ICM located away from the cytoplasmic membrane and extending into the cytoplasm are present in Type I methylotrophs. In Type II methylotrophs, the ICM form pairs of peripheral membranes located parallel to the cytoplasmic membrane. Complex cell wall structures of tightly packed cup-shaped subunits have been described in strains of marine and freshwater phototrophic sulfur bacteria and several strains of methane oxidizing bacteria. We examined the ultrastructure of the methylotrophs with particular view of the ICM and surface structural features, between representatives of the Type I Methylomonas albus (BG8), and Type II Methylosinus trichosporium (OB-36).

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