On quadratic residue codes and hyperelliptic curves

A long standing problem has been to develop "good" binary linear codes to be used for error-correction. This paper investigates in some detail an attack on this problem using a connection between quadratic residue codes and hyperelliptic curves. One question which coding theory is used to attack is: Does there exist a c<2 such that, for all sufficiently large $p$ and all subsets S of GF(p), we have |X_S(GF(p))| < cp?Comment: 18 pages, no figure

A primer on computational group homology and cohomology

These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You should know the definition of a (left) module over a (non-commutative) ring, what \zzz[G] is (where $G$ is a group written multiplicatively and \zzz denotes the integers), and some ring theory and group theory. However, an attempt has been made to (a) keep the presentation as simple as possible, (b) either provide an explicit reference of proof of everything. Several computer algebra packages are used to illustrate the computations, though for various reasons we have focused on the free, open source packages such as GAP and SAGE.Comment: 40+ pages. To appear in conference for the 60th birthday of Tont Gaglion

Automorphism groups of some AG codes

We show that in many cases, the automorphism group of a curve and the permutation automorphism group of a corresponding AG code are the same. This generalizes a result of Wesemeyer beyond the case of planar curves.Comment: added a reference, fixed error in remark