Any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring. The theory of Griihner bases for modules gives a compact description and implementation of a systematic encoder. We present examples of algebraic-geometric Goppa codes that can be encoded by these methods, including the one-point Hermitian codes. Index TermsSystematic encoding, algebraic-geometr...

The principal result described in this report is the design and implementation of a parallel version of Buchberger's algorithm. Its correctness is stated and some experimental results are given. The first parts are devoted to a partial review of Grobner bases, of Buchberger's algorithm which computes them, and of some of their applications.

This paper discusses a result by Fliess about input-output equations [or polynomial systems with time delays, and strengthens the result somewhat. The proof given is more detailed and opens the way [or constructive methods [or determining the input-output behavior. Some such methods based on Grobner bases are described in detail. Furthermore, some connections with observability are exploited.

Grabner basis is olle of the most important tools ill recent symbolic algebraic computations. Howe\'er, computing a Grobncr basis fo r the given polynomial ideal is lIot easy and it is lIot numcric.. . l1y stable if polynomials have inexact coefficients. I n this paper, we study what we should get for computing a Grabner basis with inexact coefficients alld introduce a naive method to compute a...

Using an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels ∏ (i,j)∈η(1 − xiyj) −1, where the product is over all cell-coordinates (i, j) of the stair-type partition shape η, consisting of the cells in a NW-SE diagonal of a rectangle diagram and below it, containing the biggest s...