Titlebook: Algebraic Algorithms and Error-Correcting Codes; 3rd International Co Jacques Calmet Conference proceedings 1986 Springer-Verlag Berlin Hei

Infirm

Government Spending and National SavingWe introduce and characterize pseudo-triple-sum-sets as a natural extension of triple-sum-sets. We Show that if Ω is the set of coordinate forms of a linear projective code C(n,k) over F=GF(q) and if .=F. Ω is a pseudo-triple-sum-set then C can be considered as a three classes association subscheme of the Hamming scheme H(n,q).

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growth-factor

interlude

limber

Some algebraic tools for error-correcting codes,We give several algebraic techniques, useful for the study of error-correcting codes : decomposition of ideals, automorphisms. We also prove that codes with coefficients in a noetherian ring are not better than codes with coefficients in a field.

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Software simulation of data transmission using error-correcting codes, through an awgn channel,We present here results obtained by simulation of error-correcting codes. The software was developed for a Research and Development Program sponsored by CNES (Centre National d‘Etudes Spatiales), on the use of error correcting codes in space communications..The results give performances of both convolutional and Reed-Solomon codes.

Horizon

On s-sum-sets and projective codes,We introduce and characterize s-sum-sets which are a natural extension of partial-difference-sets and triple-sum-sets. We show that if Ω is the set of coordinate forms of .(n,k) and if X=F*Ω is an s-sum-set then .(n,k) has not more than three non-zero distinct weights.

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煤渣

A decoding algorithm for linear codes,A decoding algorithm for linear codes is presented, which is able to correct beyond the half minimum distance and which has the capability to include soft decision decoding. Results on applying this algorithm to some codes (with and without soft decision) are included.

occurrence

Recent results on coding and algebraic geometry,Construction of GOPPA geometric codes from algebraic curves and some results on these codes improving VARCHAMOV-GILBERT bound are presented. We consider also the particular case of elliptic algebraic curves.