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Z2Z4-linear codes

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Z2Z4-linear codesby Joaquim Borges ... [et al.].
其他題名:	ℤ2ℤ4-linear codes
其他作者:	Borges, Joaquim.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xii, 245 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Coding theory.
電子資源:	https://doi.org/10.1007/978-3-031-05441-9
ISBN:	9783031054419$q(electronic bk.)

Z2Z4-linear codes
Z2Z4-linear codes[electronic resource] /ℤ2ℤ4-linear codesby Joaquim Borges ... [et al.]. - Cham :Springer International Publishing :2022. - xii, 245 p. :ill., digital ;24 cm.

1 Introduction -- 2 ℤ2ℤ4-Additive and ℤ2ℤ4-Linear Codes -- 3 Duality of ℤ2ℤ4-Additive Codes -- 4 ℤ2ℤ4-Additive Self-Dual Codes -- 5 Linearity, Rank and Kernel -- 6 Families of ℤ2ℤ4-Additive Codes -- 7 ℤ2ℤ4-Additive Cyclic Codes -- 8 Encoding and Decoding ℤ2ℤ4-Linear Codes -- 9 Generalizations and Applications of ℤ2ℤ4-Additive Codes.

The theory developed for ℤ2ℤ4-additive codes is the starting point for much generalization about codes over mixed alphabets. They have opened a new, emergent area of research. The techniques used for ℤ2ℤ4-linear codes are being generalized and applied to more general codes. By example, these codes have contributed to the classification of many nonlinear codes. Moreover, they can be considered as the starting point of many different generalizations given over mixed alphabets, thereby representing a useful area of research. Since 2010, more than 30 papers have been published about the codes considered in the book, which includes important classes of binary codes (1-perfect, Hadamard, etc.) that are not linear in general. For example, much recent research has shown the application of the techniques described for the family of cyclic ℤ2ℤ4-linear codes. Topics and Features: Examines everything from the basic definitions to very advanced results Provides numerous examples, succinctly and comprehensively gathering and using the relevant information Includes examples using commands from a new Magma package, developed mostly by the same authors Proposes algorithms, for instance to describe coding and decoding strategies This unique volume will be eminently suitable for researchers working on coding theory over rings, especially over mixed alphabets. Experts will find commands and algorithms that will be useful in the generalization to codes over mixed alphabets. Additionally, by outlining the basic theory of codes over mixed alphabets and providing numerous examples, the book will be useful to researchers wanting to be introduced to the topic. The authors are all affiliated with the Dept. of Information and Communications Engineering at the Universitat Autònoma de Barcelona, Spain. Joaquim Borges and Cristina Fernández-Córdoba are Associate Professors, Jaume Pujol is a now retired Associate Professor, Josep Rifà is Professor Emeritus, and Mercè Villanueva is Associate Professor.

ISBN: 9783031054419$q(electronic bk.)

Standard No.: 10.1007/978-3-031-05441-9doiSubjects--Topical Terms:

184605
Coding theory.

LC Class. No.: TK5102.92

Dewey Class. No.: 003.54

Z2Z4-linear codes
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003 DE-He213
005 20220630172603.0
006 m d
007 cr nn 008maaau
008 230109s2022 sz s 0 eng d
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245 0 0 $a Z2Z4-linear codes $h [electronic resource] / $c by Joaquim Borges ... [et al.].
246 3 $a ℤ2ℤ4-linear codes
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300 $a xii, 245 p. : $b ill., digital ; $c 24 cm.
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505 0 $a 1 Introduction -- 2 ℤ2ℤ4-Additive and ℤ2ℤ4-Linear Codes -- 3 Duality of ℤ2ℤ4-Additive Codes -- 4 ℤ2ℤ4-Additive Self-Dual Codes -- 5 Linearity, Rank and Kernel -- 6 Families of ℤ2ℤ4-Additive Codes -- 7 ℤ2ℤ4-Additive Cyclic Codes -- 8 Encoding and Decoding ℤ2ℤ4-Linear Codes -- 9 Generalizations and Applications of ℤ2ℤ4-Additive Codes.
520 $a The theory developed for ℤ2ℤ4-additive codes is the starting point for much generalization about codes over mixed alphabets. They have opened a new, emergent area of research. The techniques used for ℤ2ℤ4-linear codes are being generalized and applied to more general codes. By example, these codes have contributed to the classification of many nonlinear codes. Moreover, they can be considered as the starting point of many different generalizations given over mixed alphabets, thereby representing a useful area of research. Since 2010, more than 30 papers have been published about the codes considered in the book, which includes important classes of binary codes (1-perfect, Hadamard, etc.) that are not linear in general. For example, much recent research has shown the application of the techniques described for the family of cyclic ℤ2ℤ4-linear codes. Topics and Features: Examines everything from the basic definitions to very advanced results Provides numerous examples, succinctly and comprehensively gathering and using the relevant information Includes examples using commands from a new Magma package, developed mostly by the same authors Proposes algorithms, for instance to describe coding and decoding strategies This unique volume will be eminently suitable for researchers working on coding theory over rings, especially over mixed alphabets. Experts will find commands and algorithms that will be useful in the generalization to codes over mixed alphabets. Additionally, by outlining the basic theory of codes over mixed alphabets and providing numerous examples, the book will be useful to researchers wanting to be introduced to the topic. The authors are all affiliated with the Dept. of Information and Communications Engineering at the Universitat Autònoma de Barcelona, Spain. Joaquim Borges and Cristina Fernández-Córdoba are Associate Professors, Jaume Pujol is a now retired Associate Professor, Josep Rifà is Professor Emeritus, and Mercè Villanueva is Associate Professor.
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650 1 4 $a Coding and Information Theory. $3 273763
650 2 4 $a Discrete Mathematics in Computer Science. $3 274791
650 2 4 $a Theory of Computation. $3 274475
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