Open AccessOn cyclic codes over finite chain rings
Author(s) -
. Monika,
Sucheta Dutt,
Ranjeet Sehmi
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1850/1/012010
Subject(s) - chain (unit) , class (philosophy) , set (abstract data type) , mathematics , code (set theory) , discrete mathematics , finite set , finite field , basis (linear algebra) , combinatorics , pure mathematics , computer science , physics , programming language , geometry , mathematical analysis , astronomy , artificial intelligence
Recent studies involve various approaches to establish a generating set for cyclic codes of arbitrary length over the class of Galois rings. One such approach involves the use of polynomials with minimal degree corresponding to specific subsets of the code, defined progressively. In this paper, we extend this approach to obtain a set of generators of cyclic codes over finite chain rings. Further, we observe that this set acts as a minimal strong Gröbner basis(MSGB) for the code.