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An Introduction to Ring-Linear Coding Theory 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 MacWilliams’ identities about the relation between weight enumerators. A further section is
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Gröbner Bases over Commutative Rings and Applications to Coding Theoryutative ring. For applications, we specialize to the case of a finite chain ring. We discuss and compare the main algorithms that may be implemented to compute Gröbner and (in the case of a chain ring) Szekeres-like bases. We give an account of a number of decoding algorithms for alternant codes ove
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https://doi.org/10.1007/978-3-030-35272-1on. To do this we introduce, with examples, the concept of linear codes and their parameters, in particular the Hamming distance..A fundamental subclass of linear codes is given by cyclic codes, that enjoy a very interesting algebraic structure. In fact, cyclic codes can be viewed as ideals in a res
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