Coding Theory and Applications

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This book contains a selection of papers presented at a Symposium on coding theory: "3 Journees sur le Codage," held November 24-26, 1986, in Cachan near Paris, France. It gives an account of the state of the art of research in France on Coding, ranging from rather theoretical topics like algebraic geometry and combinatorial coding to applications like modulation, real-space decoding and implementation of coding algorithms on microcomputers. The symposium was the second one of this type. With its broad spectrum, it was a unique opportunity for contacts between university and industry on the topics of information and coding theory.

Contenu
Codes and character sums.- Codes from some Artin-Schreier curves.- Families of codes exceeding the Varshamov-Gilbert bound.- Polynomial factorization using Brill-Noether algorithm.- New bounds on cyclic codes from algebraic curves.- Exponential sums and the Carlitz-Uchiyama bound.- Bounds on the use of the postal channel.- A new authentication algorithm.- A method for finding codewords of small weight.- Generating codewords in real space: Application to decoding.- Weighted decoding of linear block codes by solving a system of implicit equations.- Suboptimum weighted-output symbol-by-symbol decoding of block codes.- Results of generalized minimum distance decoding for block code of rate 1/2.- An overview of recent results in the theory of burst-correcting codes.- Note for computing the minimun polynomial of elements in large finite fields.- A quaternary cyclic code, and a family of quadriphase sequences with low correlation properties.- A simple description of Kerdock codes.- Relation between the minimum weight of a linear code over GF(qm) and its q-ary image over GF(q).- Covering in hypercubes.- More on the plane of order 10.- Linear recurrence relations and an extended subresultant algorithm.- The future pan European mobile radiotelephone system a short overview.- Experimental direct-sequence spread-spectrum digital mobile radio transmission.- Concatenated coding schemes for H.F. (High Frequency) channels.- Bandwidth efficient coding on channels disturbed by jamming and impulse noise.- Error correcting coding scheme against partial time jammers.- Evaluation of a coding design for a very noisy channel / Evaluation d'une Configuration de Codage Pour une Ligne tres Bruitee.- Design and implementation of an asynchronous transmission process by code division multiple access.- Is minimal distance a good criterion?.- Open problem 1: Covering radius of the circuit code.- Open problem 2: Cyclic codes over rings and p-adic fields.