{"product_id":"z2z4-linear-codes-9783031054402","title":"Z2z4-Linear Codes","description":"\u003cp\u003e • Author(s): Joaquim Borges\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Information Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThe theory developed for \u003cb\u003eℤ\u003c\/b\u003e\u003csub\u003e2\u003c\/sub\u003e\u003cb\u003eℤ\u003c\/b\u003e\u003csub\u003e4\u003c\/sub\u003e-additive codes is the starting point for much generalization about codes over mixed alphabets. They have opened a new, emergent area of research. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe techniques used for \u003cb\u003eℤ\u003c\/b\u003e\u003csub\u003e2\u003c\/sub\u003e\u003cb\u003eℤ\u003c\/b\u003e\u003csub\u003e4\u003c\/sub\u003e-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 ℤ\u003csub\u003e2\u003c\/sub\u003eℤ\u003csub\u003e4\u003c\/sub\u003e-linear codes. \u003c\/p\u003e\u003cp\u003e\u003cb\u003e\u003ci\u003eTopics and Features\u003c\/i\u003e\u003c\/b\u003e: \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eExamines everything from the basic definitions to very advanced results \u003c\/li\u003e\n\u003cli\u003eProvides numerous examples, succinctly and comprehensively gathering and using the relevant information \u003c\/li\u003e\n\u003cli\u003eIncludes examples using commands from a new Magma package, developed mostly by the same authors \u003c\/li\u003e\n\u003cli\u003eProposes algorithms, for instance to describe coding and decoding strategies\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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. \u003c\/p\u003e\u003cp\u003eThe authors are all affiliated with the Dept. of Information and Communications Engineering at the Universitat Autònoma de Barcelona, Spain. \u003cb\u003eJoaquim Borges \u003c\/b\u003eand \u003cb\u003eCristina Fernández-Córdoba \u003c\/b\u003eare Associate Professors, \u003cb\u003eJaume Pujol\u003c\/b\u003e is a now retired Associate Professor, \u003cb\u003eJosep Rifà \u003c\/b\u003eis Professor Emeritus, and \u003cb\u003eMercè Villanueva \u003c\/b\u003eis Associate Professor.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45275325431959,"sku":"9783031054402","price":10187.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783031054402.webp?v=1769282581","url":"https:\/\/atlanticbooks.com\/products\/z2z4-linear-codes-9783031054402","provider":"Atlantic Books","version":"1.0","type":"link"}