• Publications
  • Influence
On the key equation
  • P. Fitzpatrick
  • Computer Science, Mathematics
    IEEE Trans. Inf. Theory
  • 1 September 1995
TLDR
A general algorithm is derived for solving the congruence a≡bg mod xn for a range of term orders defined by the conditions on the particular solution required, inspired by the key equation for alternant codes.
Algebraic structure of quasicyclic codes
Orientability of Fredholm families and topological degree for orientable nonlinear Fredholm mappings
Abstract We construct a degree theory for oriented Fredholm mappings of index zero between open subsets of Banach spaces and between Banach manifolds. Our approach is based on the orientation of
Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems
We develop an integer valued degree theory for quasilinear Fredholm maps. This class of maps is large enough so we can place in this framework all fully nonlinear elliptic boundary value problems
Gröbner bases and combinatorics for binary codes
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gröbner basis of this ideal with respect to a total degree ordering. In the first
Parity and generalized multiplicity
Assuming that X and Y are Banach spaces and a:(a, b) —» ?2?(X, Y) is a path of linear Fredholm operators with invertible endpoints, in (F-Pl) we defined a homotopy invariant of a, a(a, I) G Z2 , the
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