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

• Main Authors: Ling, San, Özbudak, Ferruh
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics
• Online Access: https://hdl.handle.net/10356/93854; http://hdl.handle.net/10220/7626
• Institution: Nanyang Technological University

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 pm+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(pm − 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.