Improved p-ary codes and sequence families from Galois rings of characteristic p(2)


LİNG S., Ozbudak F.

SIAM JOURNAL ON DISCRETE MATHEMATICS, vol.19, no.4, pp.1011-1028, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 4
  • Publication Date: 2006
  • Doi Number: 10.1137/s089548010444506x
  • Title of Journal : SIAM JOURNAL ON DISCRETE MATHEMATICS
  • Page Numbers: pp.1011-1028

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 F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m(D-[D/p2])), where 1 <= D <= p(m/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 p(m) - 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.