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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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发表于 2025-3-21 16:28:25 | 显示全部楼层 |阅读模式
期刊全称Algebraic Coding Theory Over Finite Commutative Rings
影响因子2023Steven T. Dougherty
视频videohttp://file.papertrans.cn/153/152559/152559.mp4
发行地址Presents the foundations required to study codes over rings.Offers generalizations of the classical bounds of coding theory.Gives a complete proof of the generalized MacWilliams relations for codes ov
学科分类SpringerBriefs in Mathematics
图书封面Titlebook: Algebraic Coding Theory Over Finite Commutative Rings;  Steven T. Dougherty Book 2017 The Author(s) 2017 algebraic coding theory.frobenius
影响因子.This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account 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 Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory..Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work..
Pindex Book 2017
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发表于 2025-3-21 20:30:30 | 显示全部楼层
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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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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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.
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