Commenced in January 2007
Paper Count: 30850
Pontrjagin Duality and Codes over Finite Commutative Rings
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332240Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1435
 J. Wood J. Duality for modules over finite rings and applications to coding theory. Amer. J. Math. 121, pp. 555-575 (1999).
 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.
 C. W. Curtis and I. Reiner. Representation Theory of Finite Groups and Associative Algebras. Interscience Publishers, 1962.
 H. Stichtenoth. Algebraic Function Fields and Codes. Springer, 1993.
 S. T. Dougherty and H. Liu, Independence of vectors in codes over rings, Designs, Codes and Cryptography, Volume 51, Number 1, 55-68, 2009.
 M. F. Atiyah and I. G. Macdonald. Introduction to commutative Algebra. Addison-Wesley, 1969.
 W. Rudin. Fourier Analysis on Groups, Wiley-Interscience, 1990.
 M. Giorgetti and A. Previtali. Galois invariance, traces codes and subfield subcodes. Finite Fields and Their Applications 16(2): 96-99 (2010).
 B. A. McDonald. Finite Rings with Identity. Marcel Dekker, 1974.