393 research outputs found
Self-Dual Codes
Self-dual codes are important because many of the best codes known are of
this type and they have a rich mathematical theory. Topics covered in this
survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight
enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems,
bounds, mass formulae, enumeration, extremal codes, open problems. There is a
comprehensive bibliography.Comment: 136 page
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
A new family of exceptional rational functions
For each odd prime power q, we construct an infinite sequence of rational
functions f(X) in F_q(X), each of which is exceptional, which means that for
infinitely many n the map c-->f(c) induces a bijection of P^1(F_{q^n}).
Moreover, each of our functions f(X) is indecomposable, which means that it
cannot be written as the composition of lower-degree rational functions in
F_q(X). In case q is not a power of 3, these are the first known examples of
indecomposable exceptional rational functions f(X) over F_q which have
non-solvable monodromy groups and have arbitrarily large degree. These are also
the first known examples of wildly ramified indecomposable exceptional rational
functions f(X), other than linear changes of polynomials.Comment: 16 page
- …