國立虎尾科技大學 |

Z2Z4-Linear Codes

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Z2Z4-Linear Codes/ by Joaquim Borges, Cristina Fernández-Córdoba, Jaume Pujol, Josep Rifà, Mercè Villanueva.
作者:	Borges, Joaquim.
其他作者:	Villanueva, Mercè.
面頁冊數:	XII, 245 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Theory of Computation. -
電子資源:	https://doi.org/10.1007/978-3-031-05441-9
ISBN:	9783031054419

Z2Z4-Linear Codes
Borges, Joaquim.

Z2Z4-Linear Codes[electronic resource] /by Joaquim Borges, Cristina Fernández-Córdoba, Jaume Pujol, Josep Rifà, Mercè Villanueva. - 1st ed. 2022. - XII, 245 p. 1 illus.online resource.

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

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

669322
Theory of Computation.

LC Class. No.: QA268

Dewey Class. No.: 003.54

Z2Z4-Linear Codes
LDR:03824nam a22004335i 4500 001 1088025
003 DE-He213
005 20220630172603.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031054419 $9 978-3-031-05441-9
024 7 $a 10.1007/978-3-031-05441-9 $2 doi
035 $a 978-3-031-05441-9
050 4 $a QA268
050 4 $a Q350-390
072 7 $a GPJ $2 bicssc
072 7 $a GPF $2 bicssc
072 7 $a COM031000 $2 bisacsh
072 7 $a GPJ $2 thema
072 7 $a GPF $2 thema
082 0 4 $a 003.54 $2 23
100 1 $a Borges, Joaquim. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1395146
245 1 0 $a Z2Z4-Linear Codes $h [electronic resource] / $c by Joaquim Borges, Cristina Fernández-Córdoba, Jaume Pujol, Josep Rifà, Mercè Villanueva.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XII, 245 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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.
650 2 4 $a Theory of Computation. $3 669322
650 2 4 $a Discrete Mathematics in Computer Science. $3 670123
650 1 4 $a Coding and Information Theory. $3 669784
650 0 $a Computer science. $3 573171
650 0 $a Discrete mathematics. $3 1254302
650 0 $a Computer science—Mathematics. $3 1253519
650 0 $a Information theory. $3 595305
650 0 $a Coding theory. $3 561460
700 1 $a Villanueva, Mercè. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1395150
700 1 $a Rifà, Josep. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1395149
700 1 $a Pujol, Jaume. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1395148
700 1 $a Fernández-Córdoba, Cristina. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1395147
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031054402
776 0 8 $i Printed edition: $z 9783031054426
776 0 8 $i Printed edition: $z 9783031054433
856 4 0 $u https://doi.org/10.1007/978-3-031-05441-9
912 $a ZDB-2-SCS
912 $a ZDB-2-SXCS
950 $a Computer Science (SpringerNature-11645)
950 $a Computer Science (R0) (SpringerNature-43710)