Improved p-ary codes and sequence families from galois rings of characteristic p2

Abstract

This paper explores the applications of a recent bound on some Weil-type exponential sums over Galois rings in the construction of codes and sequences. A family of codes over ℱp, mostly nonlinear, of length p m+1 and size p2 · pm(D-[D/p2]) where 1 ≤ D ≤ pm/2, is obtained. The bound on this type of exponential sums provides a lower bound for the minimum distance of these codes. Several families of pairwise cyclically distinct p-ary sequences of period p(p m-1) of low correlation are also constructed. They compare favorably with certain known p-ary sequences of period pm-1. Even in the case p = 2, one of these families is slightly larger than the family Q(D) in section 8.8 in [T. Helleseth and P. V. Kumar, Handbook of Coding Theory, Vol. 2, North-Holland, 1998, pp. 1765-1853], while they share the same period and the same bound for the maximum nontrivial correlation. © 2006 Society for Industrial and Applied Mathematics.