Codes of Polynomial Type

Authors:

Mohammed Sabiri,

DOI NO:

https://doi.org/10.26782/jmcms.2019.04.00028

Keywords:

Cyclic codes,dual code,Polynomial code, principal polynomial code,codes of polynomial type,

Abstract

In this work we try to introduce the concept of codes of polynomial type and polynomial codes that are built over the ring A[X]/A[X]f(X).It should be noted that for particular cases of f we will find some classic codes for example cyclic codes, constacyclic codes, So the study of these codes is a generalization of linear codes.

Refference:

I.Adamek, J. (1991). Foundations of coding. Interscience, Prague.

II.Greferath, M. (1997). Cyclic codes over finite rings. Discrete Mathematics 177, University of Duisburg.

III.Klein, P. N. (2013). Coding the Matrix: Linear Algebra through Computer Science Applications. Newtonian Press, Brown, first edition.

IV.Neubauer, A., Freudenberger, J., and Kuhn,

V. (2007). Coding Theory -Algorithms, Architectures, and Applications.Wiley-Interscience, Germany.

V.Springer, Eindhoven University, third edition.

VI.van Lint, J. (1973). Coding Theory. Springer-Verlag Berlin Heidelberg, London, 2nd edition.

VII.van Lint, J. (1999). Introduction to Coding Theory.VIII.Williams, F. M. and Sloane, N. J. A. (1981). The theory of error-corecting codes. Mathematical Library, North-Holland, third edition

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