Improved p-ary codes and sequence families from Galois rings of characteristic p2
Date of Issue2006
School of Physical and Mathematical Sciences
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.
SIAM Journal of discrete mathematics
©2006 Society for Industrial and Applied Mathematics. This paper was published in SIAM J Discrete Math and is made available as an electronic reprint (preprint) with permission of Society for Industrial and Applied Mathematics.The paper can be found at http://dx.doi.org/10.1137/S089548010444506x. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.