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Title: Improved p-ary codes and sequence families from galois rings of characteristic p2
Authors: Ling, S. 
Özbudak, F.
Keywords: Exponential sum
Galois rings
p-ary code
p-ary sequence
Issue Date: 2005
Citation: Ling, S., Özbudak, F. (2005). Improved p-ary codes and sequence families from galois rings of characteristic p2. SIAM Journal on Discrete Mathematics 19 (4) : 1011-1028. ScholarBank@NUS Repository.
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.
Source Title: SIAM Journal on Discrete Mathematics
ISSN: 08954801
DOI: 10.1137/S089548010444506X
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