Algebraic Coding First French-Soviet Workshop, Paris, July 22-24, 1991. Proceedings

This volume presents the proceedings of the first French-Soviet workshop on algebraic coding, held in Paris in July 1991. The idea for the workshop, born in Leningrad (now St. Petersburg) in 1990, was to bring together some of the best Soviet coding theorists. Scientists from France, Finland, Germany, Israel, Italy, Spain, and the United States also attended. The papers in the volume fall rather naturally into four categories: - Applications of exponential sums - Covering radius - Constructions -Decoding.

On the correlation of sequences.- On Gaussian sums for finite fields and elliptic curves.- Exponential sums and constrained error-correcting codes.- Constructions of codes with covering radius 2.- On perfect weighted coverings with small radius.- An extremal problem related to the covering radius of binary codes.- Bounds on covering radius of dual product codes.- Remarks on greedy codes.- On nonbinary codes with fixed distance.- Saddle point techniques in asymptotic coding theory.- Non-binary low rate convolutional codes with almost optimum weight spectrum.- Position recovery on a circle based on coding theory.- The lower bound for cardinality of codes correcting errors and defects.- Soft decoding for block codes obtained from convolutional codes.- Partial ordering of error patterns for maximum likelihood soft decoding.- A fast matrix decoding algorithm for rank-error-correcting codes.- A fast search for the maximum element of the fourier spectrum.- Coding theorem for discrete memoryless channels with given decision rule.- Decoding for multiple-access channels.