Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

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.