Oscar Moreno

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Let p be an odd prime, n 2 2 be an integer, and w be a complex primitive pth root of unity. A construction is presented for a family of p" p-phase sequences (symbols of the form ai), where each sequence has length p" 1, and where the maximum nontrivial correlation value C,, does not exceed 1+@. A complete distribution of correlation values is provided. As a(More)
Many research groups have described genetic networks as networks of Boolean variables. We will show that these Boolean network models are examples of Finite Dynamical Systems (FDS), and we will generalize Boolean networks to finite fields, which we call finite field genetic network models. We also show two different methods to construct these FDS models(More)
At the present time, there are very good methods to obtain bounds for the minimum distance of BCH codes and their duals. On the other hand, there are few other bounds suitable for general cyclic codes. Therefore, research Problem 9.9 of MacWilliams and Sloane, The Theory of Error-Correcting Codes, asks if the bound of Deligne for exponential sums in several(More)
Optical orthogonal codes (OOC) are used as spreading sequences for optical CDMA networks. An OOC is a family of constant weight binary codes with a pre-specified maximum correlation parameter (MCP). Johnson in his 1962 paper introduced three bounds for constant weight codes, that we call bounds A, B, and hybrid. Subsequently Chung et al. adapted Johnson(More)
In 1935, C. Chevalley proved a conjecture by E. Artin: if F ðX1; . . . ; XmÞ is a homogeneous polynomial of total degree d < m over a 7nite 7eld Fq having q 1⁄4 p elements, then F has a non-trivial zero. Chevalley showed the result to hold even when the homogeneity hypothesis is replaced by the weaker requirement that F ðX1; . . . ; XmÞ has no constant(More)