Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 10th International Symposium,AAECC-10 San Juan de Puerto Rico, Puerto Rico, May 10–14, 1993 Proceedings

A. R. Calderbank, P. C. Fishburn (auth.), Gérard Cohen, Teo Mora, Oscar Moreno (eds.)3540566864, 9783540566861

This volume is the proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 10),held in Puerto Rico, May 1993. The aim of the AAECC meetings is to attract high-level research papers and to encourage cross-fertilization among different areas which share the use of algebraic methods and techniques for applications in the sciences of computing, communications, and engineering. The AAECC symposia are mainly devoted to research in coding theory and computer algebra. The theoryof error-correcting codes deals with the transmission of information in the presence of noise. Coding is the systematic use of redundancy in theformation of the messages to be sent so as to enable the recovery of the information present originally after it has been corrupted by (not too much)noise. Computer algebra is devoted to the investigation of algorithms, computational methods, software systems and computer languages, oriented to scientific computations performed on exact and often symbolic data, by manipulating formal expressions by means of the algebraic rules they satisfy. Questions of complexity and cryptography are naturally linked with both coding theory and computer algebra and represent an important share of the area covered by AAECC.

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Table of contents :
Sequence based methods for data transmission and source compression….Pages 1-12
On the apparent duality of the Kerdock and Preparata codes….Pages 13-24
Bounds for codes as solutions of extremum problems for systems of orthogonal polynomials….Pages 25-42
Systems of algebraic equations solved by means of endomorphisms….Pages 43-56
Criteria for sequence set design in CDMA communications….Pages 57-65
Using Groebner bases to determine the algebraic and transcendental nature of field extensions: Return of the killer tag variables….Pages 66-75
A “Divide and conquer” algorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals….Pages 76-88
An efficient algorithm for the sparse mixed resultant….Pages 89-104
Some features of binary block codes for correcting asymmetric errors….Pages 105-120
Fixed-parameter complexity and cryptography….Pages 121-131
A class of algebraic geometric codes from curves in high-dimensional projective spaces….Pages 132-146
A new class of sequences: Mapping sequences….Pages 147-161
A zero-test and an interpolation algorithm for the shifted sparse polynomials….Pages 162-169
Parallelization of quantifier elimination on a workstation network….Pages 170-179
Hyperplane sections of fermat varieties in P 3 in char. 2 and some applications to cyclic codes….Pages 180-194
Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems….Pages 195-212
Relations among Lie formal series and construction of symplectic integrators….Pages 213-230
Exponential sums as discrete fourier transform with invariant phase functions….Pages 231-243
Application of finite fields to memory interleaving….Pages 244-256
An elementary proof of a partial improvement to the Ax-Katz Theorem….Pages 257-268
Energy functions associated with error-correcting codes….Pages 269-278
On determining all codes in semi-simple group rings….Pages 279-290
On hyperbolic cascaded Reed-Solomon codes….Pages 291-303
Peak-shift and bit error-correction with channel side information in runlength-limited sequences….Pages 304-315
On a third order differential equation whose differential Galois group is the simple group of 168 elements….Pages 316-324
Approximating the number of error locations within a constant ratio is NP -complete….Pages 325-331
Two chosen-plaintext attacks on the Li-Wang joint authentication and encryption scheme….Pages 332-343
Some constructions of perfect binary codes….Pages 344-354