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TitleAn introduction to ring-linear coding theory.
Author(s) Marcus Greferath
TypeBook, Chapter in Book, Conference Proceeding
AbstractThis contribution gives an introduction to algebraic coding theory over rings. We will start with a historical sketch and then present basics on rings and modules. Particular attention will be paid to weight functions on these, before some foundational results of ring-linear coding will be discussed. Among these we will deal with code equivalence, and with MacWilliamsí identities about the relation between weight enumerators. A further section is devoted to existence bounds and code optimality. An outlook will then be presented on the still unsolved problem of the construction of large families of ring-linear codes of high quality.
ISBN978-3-540-93805-7/hbk; 978-3-5
URL http://link.springer.com/chapter/10.1007%2F978-3-540-93806-4_13
PublisherBerlin: Springer
Translation No
Refereed No