This volume contains the proceedings of the 4th International Conference on Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra (AAECC-4), held in Karlsruhe, 23-26 September, 1986. Selected papers which were given at the conference have been reviewed a second time and are presented here.
The present volume contains the proceedings of the AAECC-5 Conference held at Menorca (Balearic Islands), June 15-19, 1987. The annual International AAECC Conference covers a range of topics related to Applied Algebra, Error-Correcting Codes, Finite Algebraic Structures, Computational Methods and Complexity in Algebra and Geometry. For the AAECC-5 Conference 73 papers were presented. Out of these thirty papers were selected for publication in the proceedings. They deal with topics such as error correcting codes (concerning problems of covering radius, decoding methods, expert systems and general results in coding theory), computational algebra, Gröbner basis, complexity, finite algebra and graphs. The proceedings of the 6th conference are published as Vol. 357 of the Lecture Notes in Computer Science.
The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.
This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
In 1988, for the first time, the two international conferences AAECC-6 and ISSAC'88 (International Symposium on Symbolic and Algebraic Computation, see Lecture Notes in Computer Science 358) have taken place as a Joint Conference in Rome, July 4-8, 1988. The topics of the two conferences are in fact widely related to each other and the Joint Conference presented a good occasion for the two research communities to meet and share scientific experiences and results. The proceedings of the AAECC-6 are included in this volume. The main topics are: Applied Algebra, Theory and Application of Error-Correcting Codes, Cryptography, Complexity, Algebra Based Methods and Applications in Symbolic Computing and Computer Algebra, and Algebraic Methods and Applications for Advanced Information Processing. Twelve invited papers on subjects of common interest for the two conferences are divided between this volume and the succeeding Lecture Notes volume devoted to ISSACC'88. The proceedings of the 5th conference are published as Vol. 356 of the Lecture Notes in Computer Science.
