In this paper, we propose a class of 2k-variable Boolean functions which have optimal algebraic degree, very high nonlinearity, and are 1-resilient. Based on our newly proposed conjecture, it can be shown that the algebraic immunity of our functions is at least suboptimal. Moreover, when k is odd, the algebraic immunity is actually optimal, and for even k, we find that the algebraic immunity is...

In this paper, Multi-Microgrids (MMG) are considered as future smart distribution grids, in which small scale energy resources (SSER) are main power generation units with small scales. Optimal operation of microgrids in defined intervals is carried out to achieve economic conditions in distribution systems. The defined operating problem is optimized using a heuristic algorithm considering uncer...

In this paper, we investigate erasure-resilient codes coming from Steiner 2-designs with block size k which can correct up to any k erasures. In view of applications it is desirable that such a code can also correct as many erasures of higher order as possible. Our main result is that the erasure-resilient code constructed from an affine space with block size q – a special Steiner 2-design – ca...

This paper presents an algorithm for optimal resilient allocation of Mobile Energy Storage Systems (MESSs) active distribution system considering the microgrids coordinated bidding process. The main contribution this is that impacts biddings on MESSs in day-ahead and real-time markets are investigated. proposed optimization framework another decomposes process into multiple procedures horizons....

We introduce new constructions of systematic authentication codes over finite fields and Galois rings. One code is built over finite fields using resilient functions and it provides optimal impersonation and substitution probabilities. Other two proposed codes are defined over Galois rings, one is based on resilient maps and it attains optimal probabilities as well, while the other uses maps wh...

We extend the notions of correlation-immune functions and resilient functions to functions over any finite alphabet. A previous result due to Gopalakrishnan and Stinson is generalized as we give an orthogonal array characterization, a Fourier transform and a matrix characterization for correlation-immune and resilient functions over any finite alphabet endowed with the structure of an Abelian g...

In June 2004, the IEEE approved a new standard for Resilient Packet Rings (RPR). The standard is maintained in the 802 LAN/MAN Standards Committee, and is designated the standard number 802.17. In this paper, we analyze and discuss performance aspects of the Resilient Packet Ring fairness mechanism. We explain that, if the ring is not configured correctly, the fairness mechanism fails to stabil...