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Codes and information. (English. Russian original) Zbl 0578.94011
Russ. Math. Surv. 39, No. 1, 87-141 (1984); translation from Usp. Mat. Nauk 39, No. 1(235), 77-120 (1984).
”The present survey is concerned with results in coding and information theory obtained in the last decade. The two main themes around which the exposition is centred are the reduction of the Hamming problem to the Riemann problem, and of the Shannon problem to the Hamming problem... The survey contains three chapters and does not assume familiarity with coding theory, information theory, or algebraic geometry. The first chapter, ”Algebraic curves”, is a short introduction to the theory of curves. The emphasis is on the computational side of the theory in the case of a finite ground field.... The second chapter, ”Error-correcting codes”, introduces the basic concepts of coding theory and traces the path followed by this theory in its move towards algebraic geometry. In the third chapter, ”Information and symmetry”, an attempt is made to construct a theory of information after the pattern of physical theories on the basis of symmetry and conservation laws.” (From the introduction).
Reviewer: P.Reichensperger

MSC:
94B05 Linear codes, general
94A15 Information theory (general)
14H05 Algebraic functions and function fields in algebraic geometry
14H25 Arithmetic ground fields for curves
94B35 Decoding
94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
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