MỘT SỐ ỨNG DỤNG VÀ MỞ RỘNG CỦA MÃ CONSTACYCLIC
Keywords
Cyclic code, negacyclic codes, constacyclic codes, repeated-root codes, dual codes, codes over finite rings,, Hamming distance, homogeneous distance, Lee distanc, Euclidean distance, chain rings, Galois rings.
Abstract
The foundations and theoretical framework of algebraic coding theory are discussed with a particular focus on cyclic and negacyclic codes over finite commutative chain rings. The crucial role of finite rings as alphabets in coding theory is highlighted. Various directions for enhancing the capabilities of cyclic and negacyclic codes in general are discussed. This paper provides an introduction to this research field and explores future research directions.
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