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

Palpate

Lyndon Benke,Michael Papasimeon,Tim MillerIn this chapter, we study polycyclic, negacyclic, constacyclic, quasicyclic and skew cyclic codes which are all generalizations of the important family of cyclic codes. We describe their algebraic setting and show how to use this setting to classify these families of codes.

宏偉

不整齊

啟發(fā)

法律

https://doi.org/10.1007/978-3-319-59806-2algebraic coding theory; frobenius rings; MacWilliams relations; codes over rings; codes over finite rin

Contend

Ring Theory,robenius rings and characterize them in terms of characters. We prove the generalized Chinese Remainder Theorem and describe what constitutes a minimal generating set for a code over a finite Frobenius ring.

新娘

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.

人類學(xué)家

灰姑娘

Fabio Fossa,Luca Paparusso,Francesco Braghinrobenius rings and characterize them in terms of characters. We prove the generalized Chinese Remainder Theorem and describe what constitutes a minimal generating set for a code over a finite Frobenius ring.

Mundane

Shrey Verma,Simon Parkinson,Saad Khanults 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.