Applied Algebra, Algebraic Algorithms and Error-Correcting Codes de Gerard Cohen

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Gerard Cohen

Teo Mora

Oscar Moreno

en Limba Engleză Paperback – 20 apr 1993

This volume is the proceedings of the 10th InternationalSymposium on Applied Algebra, Algebraic Algorithms andError-Correcting Codes (AAECC 10),held in Puerto Rico, May1993.The aim of the AAECC meetings is to attract high-levelresearch papers and to encourage cross-fertilization amongdifferent areas which share the use of algebraic methods andtechniques for applications in the sciences of computing,communications, and engineering.The AAECC symposia are mainly devoted to research in codingtheory and computer algebra. The theoryof error-correctingcodes deals with the transmission of information in thepresence of noise. Coding is the systematic use ofredundancy in theformation of the messages to be sent so asto enable the recovery of the information present originallyafter it has been corrupted by (not too much)noise.Computer algebra is devoted to the investigation ofalgorithms, computational methods, software systems andcomputer languages, oriented to scientific computationsperformed on exact and often symbolic data, by manipulatingformal expressions by means of the algebraic rules theysatisfy. Questions of complexity and cryptography arenaturally linked with both coding theory and computeralgebra and represent an important share of the area coveredby AAECC.

Citește tot Restrânge

Cuprins

Sequence based methods for data transmission and source compression.- On the apparent duality of the Kerdock and Preparata codes.- Bounds for codes as solutions of extremum problems for systems of orthogonal polynomials.- Systems of algebraic equations solved by means of endomorphisms.- Criteria for sequence set design in CDMA communications.- Using Groebner bases to determine the algebraic and transcendental nature of field extensions: Return of the killer tag variables.- A “Divide and conquer” algorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals.- An efficient algorithm for the sparse mixed resultant.- Some features of binary block codes for correcting asymmetric errors.- Fixed-parameter complexity and cryptography.- A class of algebraic geometric codes from curves in high-dimensional projective spaces.- A new class of sequences: Mapping sequences.- A zero-test and an interpolation algorithm for the shifted sparse polynomials.- Parallelization of quantifier elimination on a workstation network.- Hyperplane sections of fermat varieties in P 3 in char. 2 and some applications to cyclic codes.- Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems.- Relations among Lie formal series and construction of symplectic integrators.- Exponential sums as discrete fourier transform with invariant phase functions.- Application of finite fields to memory interleaving.- An elementary proof of a partial improvement to the Ax-Katz Theorem.- Energy functions associated with error-correcting codes.- On determining all codes in semi-simple group rings.- On hyperbolic cascaded Reed-Solomon codes.- Peak-shift and bit error-correction with channel side information in runlength-limited sequences.- On athird order differential equation whose differential Galois group is the simple group of 168 elements.- Approximating the number of error locations within a constant ratio is NP-complete.- Two chosen-plaintext attacks on the Li-Wang joint authentication and encryption scheme.- Some constructions of perfect binary codes.