Group and Loop Algebras over Finite Fields

Language: English

Published by Scholars' Press Mai 2015, 2015

3639512685 / 9783639512687

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This item is printed on demand - Print on Demand Titel. Neuware -In this, the 15th year of the 21st century, the need to translate plain text into code and to transmit securely, and the plethora of uses to which encryption is applied, needs no amplification. Recent methods have produced so-called cyclic codes, which have the property that if (a_1,a_2,a_3.,a_n) is a code word, then so is the cyclic shift (a_n,a_1,a_2.,a_{n-1}). The realization that such a code is an ideal in the group algebra of a cyclic group has motivated a large body of research into using group algebras to produce codes. In this area, the central theme is ``efficiency,'' a term that describes the need to maximize simultaneously both the Hamming distance between code words and the dimension of the code. Since an ideal in a semisimple group algebra KG corresponds to a central idempotent, and since a central idempotent is the sum of idempotents that generate the simple components of KG, the need to find these simple components is clear. This is the theme of the present monograph, which will interest many algebraists, including those who study Moufang loops and alternative rings. The groups studied are the building blocks of loops whose loop rings are alternative.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 148 pp. Englisch.

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Title
Group and Loop Algebras over Finite Fields
Author
Raul Antonio Ferraz
Publisher
Scholars' Press Mai 2015
Publication year
2015
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3639512685
ISBN 13
9783639512687
Item weight
238 grams
Dimensions
220x150x10 mm

buchversandmimpf2000

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