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Improved p-ary codes and sequence families from Galois rings of characteristic p(2)
Date
2006-01-01
Author
LİNG, SAN
Özbudak, Ferruh
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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.
Subject Keywords
General Mathematics
URI
https://hdl.handle.net/11511/42175
Journal
SIAM JOURNAL ON DISCRETE MATHEMATICS
DOI
https://doi.org/10.1137/s089548010444506x
Collections
Department of Mathematics, Article
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S. LİNG and F. Özbudak, “Improved p-ary codes and sequence families from Galois rings of characteristic p(2),”
SIAM JOURNAL ON DISCRETE MATHEMATICS
, pp. 1011–1028, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42175.