**Date & Time:** Wednesday, 26th December, 2012 at 15:30 hrs.

**Venue:** Ramanujan Hall

**Title:** A lemma on polynomials modulo $p^m$ and applications to coding theory

**Speaker:** Prof. Richard Wilson, California Institute of Technology (Caltech)

**Abstract:**
An integer-valued function $f(x)$ on the integers that is periodic of period $p^e$, $p$ prime, can be matched, modulo $p^m$, by a polynomial function $w(x)$. We give an upper bound for the minimum degree of such a polynomial and give as applications a short proof of a theorem of McEliece on the divisibility of weights of codewords in $p$-ary cyclic codes by powers of $p$ and two other results on weights of codewords.