منابع مشابه
Algebraic Geometric Coding Theory
Acknowledgements Firstly, I would like to thank my supervisor, Dr David R. Kohel whose many helpful comments and patient guidance made this thesis possible. Secondly, I would like to thank David Gruenwald for volunteering his time to proofread this thesis. Almost all of his recommendations were taken on board. This thesis is the better for it. To a less extent, my thanks go to the IT school of ...
متن کاملAlgebraic Methods for Channel Coding
This work is dedicated to developing algebraic methods for channel coding. Its goal is to show that in different contexts, namely single-antenna Rayleigh fading channels, coherent and non-coherent MIMO channels, algebraic techniques can provide useful tools for building efficient coding schemes. Rotated lattice signal constellations have been proposed as an alternative for transmission over the...
متن کاملIntroduction to Algebraic Coding Theory
4 Ideals and cyclic codes 18 4.1 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Cyclic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Group of a code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Minimal polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.5 BCH and Reed-Solomon codes . . . . . . . . . . ....
متن کاملIntroduction to Algebraic Coding Theory
∗The first versions of this book were written in Fall 2001 and June 2002 at Cornell University, respectively supported by an NSF VIGRE Grant and a Department of Mathematics Grant. The current version was written in 2005 at Franklin W. Olin College of Engineering supported by NSF CCLI DUE-0410517 Grant. Edits were made in 2006 under the same grant. If you wish to use this book, please simply let...
متن کاملCoding Theory and Algebraic Combinatorics
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In particular, special interest is devoted to the relationship between codes and combinatorial designs. ...
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ژورنال
عنوان ژورنال: IEICE ESS Fundamentals Review
سال: 2015
ISSN: 1882-0875
DOI: 10.1587/essfr.8.151