An Explicit Tower over Cubic Finite Fields and Zink’s Lower Bound

Codes over Galois Ring Gilberto Bini We shall briefly recall some basic facts on trace codes over finite fields. In particular, we will focus on generalizations of dual Melas codes. After such an overview, we will introduce the Galois ring set-up in which we try to extend some of the techniques over fields. For these purposes, we need some results on exponential sums over Galois rings. Finally, we give a lower bound on the minimum Hamming distance of the generalized (Gray) image of our trace codes over rings. Weight distribution of cyclic codes Hans Dobbertin Self-Dual Divisible Codes Iwan Duursma The best known asymptotic upper bound for binary self-dual codes is due to KrasikovLitsyn (2000), with a different proof by Rains (2003). As n→∞ d e ≤ 1 2 ( 1− 1 4 √ 5 )