scholarly journals A DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY

2018 ◽  
Vol 72 (1) ◽  
pp. 123-141
Author(s):  
Michio OZEKI
Keyword(s):  
Coding Theory ◽  
Root Lattices ◽  
The Relationship

(R, S)-Norm Information Measure and A Relation Between Coding and Questionnaire Theory

2016 ◽  
Vol 23 (03) ◽  
pp. 1650015 ◽  
Author(s):  
Rajesh Joshi ◽  
Satish Kumar
Keyword(s):  
Lower Bound ◽  
Word Length ◽  
Coding Theory ◽  
Code Word ◽  
Information Measure ◽  
The Relationship

In this paper, we introduce a quantity which is called (R, S)-norm entropy and discuss some of its major properties in comparison with Shannon’s and other entropies known in the literature. Further, we give an application of (R, S)-norm entropy in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel. The theorem states that the proposed entropy is the lower bound of mean code word length. Further, we give an application of (R, S)-norm entropy and noiseless coding theorem in questionnaire theory. We show that the relationship between noiseless coding theorem and questionnaire theory through a charging scheme based on the resolution of questions and lower bound on the measure of the charge can also be obtained.

scholarly journals Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
H. D. Arora ◽  
Anjali Dhiman
Keyword(s):  
Information Theory ◽  
Data Compression ◽  
Error Correction ◽  
Coding Theory ◽  
Fuzzy Information ◽  
Fuzzy Measures ◽  
Information Measures ◽  
Codeword Length ◽  
Engineering Mathematics ◽  
The Relationship

In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of orderαand typeβfor 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established.

scholarly journals Some Applications of Coding Theory in the Projective Plane of Order Four

2019 ◽  
Vol 30 (1) ◽  
pp. 152
Author(s):  
Najm A. M. AL-Seraji ◽  
Hamza L. M. Ajaj
Keyword(s):  
Finite Field ◽  
Projective Plane ◽  
Coding Theory ◽  
Minimum Distance ◽  
Incidence Matrix ◽  
Maximum Value ◽  
Order Four ◽  
The Relationship

The main aim of this research is to introduce the relationship between the topic of coding theory and the projective plane of order four. The maximum value of size code M over the finite field of order four and an incidence matrix with the parameters, n (length of code), d (minimum distance of code) and e (error-correcting of code) have been constructed. Some examples and theorems have been given.

A QUESTION CONCERNING THE FACTORIZATION OF CYCLIC GROUPS

2007 ◽  
Vol 17 (08) ◽  
pp. 1573-1575
Author(s):  
A. D. SANDS
Keyword(s):  
Cyclic Group ◽  
Coding Theory ◽  
Cyclic Groups ◽  
Finite Cyclic Group ◽  
Factorization Theory ◽  
The Relationship

In a paper concerning the relationship between coding theory and factorization theory Restivo, Salemi, and Sportelli made a conjecture that if subsets possess certain properties then they cannot form a factorization of a finite cyclic group. In this note it is shown that in fact such factorizations do exist.

scholarly journals Fully prime double-framed soft ordered semigroups

2020 ◽  
Vol 2 (4) ◽  
pp. 17-25
Author(s):  
Tauseef Asif ◽  
Asghar Khan ◽  
Jian Tang
Keyword(s):  
Coding Theory ◽  
Finite State Machines ◽  
Formal Languages ◽  
State Machines ◽  
Ordered Semigroups ◽  
Finite State ◽  
The Relationship ◽  
Automata And Formal Languages

It is well known that semigroups are basic structures in many applied branches like automata and formal languages, coding theory, finite state machines and others. Due to these possibilities of applications, semigroups and related structures are presently extensively investigated in soft theoretic (and in fuzzy theoretic) settings. The aim of this paper, is to introduce the concepts of double-framed soft ideals (briefly, DFS ideals) over an initial universe set U. The basic characterizations of this notion are studied. Different classes of ordered semigroups are characterized by using the notions of DFS l- and r-ideals over U. The notions of prime, and irreducible double-framed soft ideals (briefly, prime and irreducible DFS ideals) over U, are investigated and the related properties are highlighted. The class of those ordered semigroups for which each DFS ideal over U is prime are studied and the relationship between prime and irreducible DFS ideals are discussed.

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Choosing a Markov blanket

2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr
Keyword(s):  
Markov Blanket ◽  
Target Article ◽  
The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

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