EUROCODE '90. International Symposium on Coding Theory and Applications, Udine, Italy, November 5-9, 1990. Proceedings (Q1189445)

Eurocode '90 starts a new series of colloquia in theory and applications of coding theory. The predecessors ``Trois Journèes sur le codage'', held in 1986 and 1988, appeared in Lecture Notes in Computer Science vols. 311 and 388. Eurocode 90 covers a very wide spectrum in modern coding theory, and the editors decide to divide the 37 contributions in eight groups, listed below. In the first three groups one finds recent results on designing algebraic, combinatorial and geometrical codes. In the algebraic section the invited paper of \textit{Th. Ericson} and \textit{V. A. Zinoviev} propose a new construction in generalized concatenation. Two papers, of \textit{M. Elia} and \textit{G. Taricco} and of \textit{T. Berger}, deal with Reed-Solomon codes and their automorphism groups, two, \textit{C. Carlet} and \textit{P. Langevin}, with open problems on Reed-Muller codes, and two papers are devoted to BCH-codes (authors \textit{F. Rodier} and \textit{D. Augier, P. Charpin, N. Sendrier}). The last one gives an algorithm to prove or disprove the existence of codewords of given length, so the authors can figure out the minimum distances of some BCH-codes. Note that they use not only algebraic ideas, Newton identities, but also powerful software like Scratchpat II. \textit{Th. Beth, D. E. Lazić} and \textit{V. Senk} present an infinite family of even self-dual codes with good distance distribution, starting with extended Hamming \([8,4,4]\) and Golay \([24,12,8]\) codes. In the combinatorial section \textit{J. Burger, H. Chabanne, M. Girault} describe some block codes which have minimum 0-1 changes, but are also well balanced. The Gray codes suffice the first but in general not the second condition. \textit{A. O. Mabogunje} and \textit{P. G. Farrell} construct from array codes some codes with different levels of protection for different parts of an information, which is in some cases better than using different codes. Two other papers deal with connections to graphs and finite fields, closer to them than to coding theory. \textit{A. Montpetit} construct codes as coherent partitions of regular connected graphs, \textit{A. Asté-Vidal} and \textit{V. Dugat} propose a construction of regular and homogeneous tournaments using Galois fields. The last ``designing'' section deals with the famous ideas about geometric codes. \textit{D. Le Brigand} shows how in some cases Pellikaan's decoding algorithm on elliptic geometric codes can be performed. Also following Pellikaan \textit{D. Rotillon} and \textit{J. A. Thiongly} describe an effective decoding procedure for Klein quartic codes. \textit{Conny Voß} shows that almost all long Goppa codes meet the Gilbert- Varshamov bound. In the last chapter of the section \textit{M. Perret} construct a nonlinear code for an algebraic curve and a divisor on it using multiplicative characters. In the section about protection of information the invited paper of \textit{M. Girault} gives a survey to the large variety of identification schemes. The connections between data hiding (cryptography) and data stabilization (coding) can also be found in the papers of \textit{S. Harari} devoted to McEliece's cryptosystems, of \textit{J. Patarin} about DES- iterations. The papers of \textit{H. J. Fell} and \textit{G. Chassé} deal with the linear complexity of finite sequences and feedback shift registers. Coding theory includes always the hard part of convolutional codes. In this section the reader finds the invited paper of \textit{D. Haccoun} on decoding techniques for these codes. He explains the basic principles and limitations of decoding procedures for convolutional codes (obligatory to read this!). \textit{R. Sfez} and \textit{G. Battail} describe a Viterbi algorithm for a concatenated scheme with inner convolutional code. \textit{R. Baldini jun.} and \textit{P. G. Farrell} present a multilevel convolutional coding method over rings. The next section on information theory starts with the invited paper of \textit{A. Sgarro} presenting a Shannon-theoretic coding theorem in authentication theory following Simmons approach. And the same author together with \textit{A. Fioretto} continue the description of a semi- entropy called fractional entropy. This section is finished with two papers on source coding. \textit{G. Battail} and \textit{M. Guazzo} compare Gallager-Huffman algorithm and Lempel-Ziv algorithm with an adaptive algorithm developed by the authors. Remarkable is the graphical representation of a source coding. \textit{R. M. Capocelli} and \textit{A. De Santis} prove a tight upper bound on the redundancy of Huffman codes in terms of the minimum codeword length and improve a result of Gallager. The last two sections are devoted to applications. \textit{A. R. Calderbank} describes in his invited paper how good covering codes can be used to make high speed data transmission more reliable. \textit{G. Battail, H. Magalhães de Oliveira} and \textit{Z. Weidong} study systems which combine coding and multilevel modulation and obtain results on maximum-distance- separable codes (MDS) to show that they are better than believed. One of the two hardware presentations is a VLSI implementation of a Reed-Solomon Coder-Decoder of a \([N,N-32]\) \((N<256)\) block code of 8-bit symbols, correcting \(x\) symbol errors and \(y\) symbol erasure if \(2x+y\leq 32\). The data rate for the [255,223]-chip is expected at 30 Mbits/s. A speeding up to 100 Mbits/s is not excluded. \textit{M. M. Darmon} and \textit{Ph. R. Sadot} propose a hybrid convolutional code system. The volume shows that coding theory is growing up and it put roots into other parts of mathematics and computer science. The more data are distributed over instable channels the more different and powerfull codings are necessary. Look for the next Eurocode. The articles of this volume will be reviewed individually. Indexed articles: \textit{Elia, M.; Taricco, G.}, A note on automorphism groups of codes and symbol error probability computation, 6-20 [Zbl 0941.94511] \textit{Berger, Thierry}, A direct proof for the automorphism group of Reed-Solomon codes, 21-29 [Zbl 0941.94512] \textit{Beth, T.; Lazić, D. E.; Šenk, V.}, A family of binary codes with asymptotically good distance distribution, 30-41 [Zbl 0941.94503] \textit{Carlet, Claude}, A transformation on Boolean functions, its consequences on some problems related to Reed-Muller codes, 42-50 [Zbl 0941.94520] \textit{Langevin, Philippe}, Covering radius of \(\text{RM}(1,9)\) in \(\text{RM}(3,9)\), 51-59 [Zbl 0941.94521] \textit{Rodier, François}, The weights of the duals of binary BCH codes of designed distance \(\delta=9\), 60-64 [Zbl 0941.94514] \textit{Augot, D.; Charpin, P.; Sendrier, N.}, The minimum distance of some binary codes via the Newton's identities, 65-73 [Zbl 0941.94513] \textit{Cohen, Gérard D.; Gargano, Luisa; Vaccaro, Ugo}, Unidirectional error detecting codes, 94-105 [Zbl 0941.94519] \textit{Astié-Vidal, Annie; Dugat, Vincent}, \(1/\lambda\)-regular and \(1/\lambda\)-homogeneous tournaments, 114-124 [Zbl 0941.05504] \textit{Le Brigand, Dominique}, Decoding of codes on hyperelliptic curves, 126-134 [Zbl 0941.94515] \textit{Rotillon, D.; Thiong Ly, J.-A.}, Decoding of codes on the Klein quartic, 135-149 [Zbl 0941.94516] \textit{Voss, Conny}, Asymptotically good families of geometric Goppa codes and the Gilbert-Varshamov bound, 150-157 [Zbl 0941.94518] \textit{Perret, Marc}, Multiplicative character sums and nonlinear geometric codes, 158-165 [Zbl 0941.94517] \textit{Harari, Sami}, A correlation cryptographic scheme, 180-192 [Zbl 0941.94508] \textit{Patarin, Jacques}, Pseudorandom permutations based on the D. E. S. scheme, 193-204 [Zbl 0941.94509] \textit{Fell, Harriet J.}, Linear complexity of transformed sequences, 205-214 [Zbl 0941.94506] \textit{Chassé, Guy}, Some remarks on an LFSR ''disturbed'' by other sequences, 215-221 [Zbl 0941.94507] \textit{Fioretto, Anna; Sgarro, Andrea}, Joint fractional entropy, 292-297 [Zbl 0941.94502]