Download Eurocode ’92: International Symposium on Coding Theory and by P. Camion, P. Charpin, S. Harari PDF

By P. Camion, P. Charpin, S. Harari

This publication is made up of the court cases of EUROCODE 1992 which was once held in Udine (Italy) on the CISM, October 27 - 30, 1992. EUROCODE ’92 is a continuation in addition to an extension of the former colloquia Trois Journèes sur le codage and EUROCODE ’90, whose complaints seemed as Lecture Notes in machine technological know-how (Volumes 388 and 514). the purpose of EUROCODE ’92 was once to draw excessive point examine papers and to motivate interchange of principles one of the parts of coding thought and similar fields which percentage an identical instruments for purposes within the technology of communications, theoretical machine technological know-how, software program engineering and arithmetic. Then the ebook is characterised through a truly large spectrum, starting from combinatories or algebraic geometry to implementation of coding algorithms. there have been approximately ninety individuals to the convention, from the tutorial and commercial worlds; fifty three meetings have been chosen. The submitted full-papers have been individually refereed for ebook via no less than foreign referees.

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1 matches he may wish to fix an integer R and construct a set of forecasts in such a way that no matter what the outcomes in the remaining ni matches are he will win at least an (R+1)st prize (provided that he is right about the i matches). In other words, he wishes to construct a code C s;; fn-i with covering radius at most R. e. l, ... l times. However, from the practical point of view what the player really wants to do is to guarantee that he wins a certain amount of money, and in that sense it is natural to attach different weights to different prizes and construct a weighted covering instead.

52 F. Levy-dit-Vehel And this because a word c' = (c 00 , co, ... , Cn-1) in Ce can be represented by the polynomial c'(X) = c00 X 0 + n-1 L: c;X";. i=O c•. We say that T. , and [0, n] \ T. is the parity set of Recall that the BCH code of length n and designed distance d over F 2 is the cyclic code with defining set : T(d) = U1

Next we obtain a lower bound on their minimum distance, that yields results for several affine-invariant codes. In particular, it gives a bound for all duals of extended BCH codes, which is interesting especially when the Carlitz-Uchiyama bound is negative. 1 Preliminaries A binary cyclic code C of length n =2m -1 is an ideal in the ring F2(Z)/(Z" -1). Let a be a primitive root in F 2 m. Then, if g(Z) is the generator polynomial of C, a; is a zero of the code C if, and only if, g(a;) 0. The set T {i E (0, n), ai is a zero of C}, is the defining set of C.

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