5 papers · 1 filter
Bounding minimum distances of cyclic codes using algebraic geometry
Nigel Boston
There are many results on the minimum distance of a cyclic code of the form that if a certain set T is a subset of the defining set of the code, then the minimum distance of the co…
Tree representations of Galois groups
Nigel Boston
Much work has gone into matrix representations of Galois groups, but there is a whole new class of naturally occurring representations that have as yet gone almost unnoticed. In fa…
Explicit computation of Galois p-groups unramified at p
Nigel Boston, Charles Leedham-Green
In this paper we introduce a new method for finding Galois groups by computer. This is particularly effective in the case of Galois groups of p-extensions ramified at finitely many…
Counterexamples to a conjecture of Lemmermeyer
Nigel Boston, Charles Leedham-Green
We produce infinitely many finite 2-groups that do not embed with index 2 in any group generated by involutions. This disproves a conjecture of Lemmermeyer and restricts the possib…
Some cases of the Fontaine-Mazur conjecture, II
Nigel Boston
This is an updated and extended version of ANT-0024. We prove more special cases of the Fontaine-Mazur conjecture regarding p-adic Galois representations unramified at p, and we pr…