Abstract
In this paper, a recent bound on some Weil-type exponential sums over Galois rings is used in the construction of codes and sequences. The bound on these type of exponential sums provides a lower bound for the minimum distance of a family of codes over \({\mathbb F}_{p}\), mostly nonlinear, of length p m + 1 and size \(p^{2} \cdot p^{m(D-\lfloor \frac {D}{p^{2}}\rceil)}\), where 1 ≤ D ≤ p m/2. 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) of [H-K, Section 8.8], while they share the same period and the same bound for the maximum non-trivial correlation.
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Ling, S., Özbudak, F. (2005). Improved p-ary Codes and Sequence Families from Galois Rings. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_16
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DOI: https://doi.org/10.1007/11423461_16
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