In the name of of Allah the Merciful

Z2Z4-Linear Codes

Joaquim Borges, Cristina Fernández-Córdoba, Jaume Pujol, Josep Rifà, Mercè Villanueva, 3031054407, 978-3031054402, 9783031054402, 978-3-031-05440-2, 978-3-031-05441-9

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English | 2022 | PDF

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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.