Commenced in January 2007
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Edition: International
Paper Count: 30172
Pontrjagin Duality and Codes over Finite Commutative Rings

Authors: Khalid Abdelmoumen, Mustapha Najmeddine, Hussain Ben-Azza

Abstract:

We present linear codes over finite commutative rings which are not necessarily Frobenius. We treat the notion of syndrome decoding by using Pontrjagin duality. We also give a version of Delsarte-s theorem over rings relating trace codes and subring subcodes.

Keywords: Codes, Finite Rings, Pontrjagin Duality, Trace Codes.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332240

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[1] J. Wood J. Duality for modules over finite rings and applications to coding theory. Amer. J. Math. 121, pp. 555-575 (1999).
[2] J. Wood J. Foundations of Linear Codes defined over Finite Modules : The extension Theorem and the MacWilliams Identities. In - Codes over Rings, Proceedings of the CIMPA Summer School, Ankara, Turkey, 18-29 August 2008, Patrick Sol, editor-, Series on Coding Theory and Crytology, Vol. 6, World Scientific, Singapore, 2009, pp. 124-190.
[3] C. W. Curtis and I. Reiner. Representation Theory of Finite Groups and Associative Algebras. Interscience Publishers, 1962.
[4] H. Stichtenoth. Algebraic Function Fields and Codes. Springer, 1993.
[5] S. T. Dougherty and H. Liu, Independence of vectors in codes over rings, Designs, Codes and Cryptography, Volume 51, Number 1, 55-68, 2009.
[6] M. F. Atiyah and I. G. Macdonald. Introduction to commutative Algebra. Addison-Wesley, 1969.
[7] W. Rudin. Fourier Analysis on Groups, Wiley-Interscience, 1990.
[8] M. Giorgetti and A. Previtali. Galois invariance, traces codes and subfield subcodes. Finite Fields and Their Applications 16(2): 96-99 (2010).
[9] B. A. McDonald. Finite Rings with Identity. Marcel Dekker, 1974.