On Calculation of Monomial Automorphisms of Linear Cyclic Codes

A description of the monomial automorphisms group of an arbitrary linear cyclic code in term of polynomials is presented. This allows us to reduce a task of code’s monomial automorphisms calculation to a task of solving some system of equations (in general, nonlinear) over a finite field. The result...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2018-09, Vol.39 (7), p.1024-1038
Main Authors: Kugurakov, V. S., Gainutdinova, A., Anisimova, T.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Automorphisms
Geometry
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Nonlinear equations
Probability Theory and Stochastic Processes
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Summary:A description of the monomial automorphisms group of an arbitrary linear cyclic code in term of polynomials is presented. This allows us to reduce a task of code’s monomial automorphisms calculation to a task of solving some system of equations (in general, nonlinear) over a finite field. The results are illustrated with examples of calculating the full monomial automorphisms groups for two codes.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080218070168