Let C be a Z2Z4-additive code of length n > 3. We prove that if the binary Gray image of C, C = Φ(C), is a 1-perfect nonlinear code, then C cannot be a Z2Z4-cyclic code except for one case of length n = 15. Moreover, we give a parity check matrix for this cyclic code. Adding an even parity check coordinate to a Z2Z4-additive 1-perfect code gives an extended 1-perfect code. We also prove that an...

We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over Fq can have. We determine it completely for q = 2, and for k = 2, and provide upper and lower bounds in the general case when both k and q are ≥ 3. A refinement L(n, k, q), as well as nonlinear analogues N(M, q) and N(n,M, q), are also introduced and studied.

Binary MDS linear codes are well-known. We prove that any binary MDS systematic non-linear code is equivalent to a linear code and hence we classify them completely.

iran is an active seismic region. earthquake damage is commonly controlled by three interacting factors including source and path characteristics, local geological and geotechnical conditions and type of the structures. obviously, all of this would require analysis and presentation of a large amount of geological, seismological and geotechnical data. in this paper, nonlinear geotechnical seismi...

This paper addresses the real-time optimal control of a Pendubot using nonlinear model predictive control (NMPC) combined with nonlinear moving horizon estimation (MHE). This fast, under-actuated nonlinear mechatronic system apparently poses a challenging benchmark problem that may benefit from a nonlinear optimization scheme. To overcome the related computational difficulties we make use of th...

Coupled theoretical and computational work is presented aimed at understanding and modeling stimulated Raman backscattering (SRBS) relevant to laser-plasma interactions (LPIs) in large-scale, nearly homogeneous plasmas. With the aid of a new code for simulating and studying the nonlinear coupling in space-time of a large number of modes, and a fluid Vlasov-Maxwell code for studying the evolutio...

Given two binary codes of length n, using Plotkin construction we obtain a code of length 2n. The construction works for linear and nonlinear codes. For the linear case, it is straightforward to see that the dimension of the final code is the sum of the dimensions of the starting codes. For nonlinear codes, the rank and the dimension of the kernel are standard measures of linearity. In this rep...

This paper examines differences in performances of a range of torsionally stiff and flexible single story buildings designed with the provisions of Iranian Standard 2800. Seismic nonlinear dynamic time history behavior of eight building models subjected to seven horizontal bi-directional design spectra compatible ground motions are investigated. These models cover a wide range of very torsional...

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