Coverings, centered codes, and combinatorial steganography
Problems of Information Transmission
Quadratic forms of codimension 2 over certain finite fields of even characteristic
Cryptography and Communications
A computability challenge: asymptotic bounds for error-correcting codes
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Ensuring message embedding in wet paper steganography
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
Finite Fields and Their Applications
Toric complete intersection codes
Journal of Symbolic Computation
Finite number of fibre products of Kummer covers and curves with many points over finite fields
Designs, Codes and Cryptography
Designs, Codes and Cryptography
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The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.