Titlebook: Algebraic Coding Theory Over Finite Commutative Rings; Steven T. Dougherty Book 2017 The Author(s) 2017 algebraic coding theory.frobenius

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MacWilliams Relations,ults of algebraic coding theory. We describe them first for codes over groups and extend this to codes over Frobenius rings. Finally, we give a practical guide for producing MacWilliams relations for a specific ring.

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PHIL

Book 2017ount on the subject..Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also

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Algebraic Coding Theory Over Finite Commutative Rings

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Infelicity

https://doi.org/10.1007/978-3-031-55044-7In this chapter, we describe families of rings including the rings of order 4, their generalizations, .-rings, and the ring .. We describe the kernel and rank of binary codes that are images of quaternary codes via the Gray map. Then a generalized Singleton bound is proven for codes over Frobenius rings.