Based on Bezout's theorem, the feasibility condition for interference alignment (IA) is established in a two-way small cell network where part of cells transmit in downlink while the others in uplink. Moreover, the sufficient and necessary condition for the two-way network to achieve as many degrees of freedom (DoFs) as the traditional one-way network is presented. We find that in certain cases every small cell can independently decide to work in either downlink mode or uplink mode as needed without causing performance degradation of IA.

Maximal designed distances for nonbinary narrow-sense quantum Bose-Chaudhuri-Hocquenghem (BCH) codes of length $n=rac{q^4-1}{r}$ and new constructions for them are given, where q is an odd prime power. These constructions are capable of designing quantum BCH codes with new parameters. Furthermore, some codes obtained here have better parameters than those constructed by other known constructions.

Let Fpm be the field of pm elements where p is an odd prime. In this letter, binary sequence pairs of period N=pm-1 are presented, where sequences are generated from the polynomial x2-c for any c Fpm{0}. The cross-correlation values of sequence pairs are completely determined, our results show that those binary sequence pairs have optimal three-level correlation.

Key predistribution schemes (KPSs) have played an important role in security of wireless sensor networks (WSNs). Due to comprehensive and simple structures, various types of combinatorial designs are used to construct KPSs. In general, compared to random KPSs, combinatorial KPSs have higher local connectivity but lower resilience against a node capture attack. In this paper, we apply two methods based on hash chains on KPSs based on transversal designs (TDs) to improve the resilience and the expressions for the metrics of the resulting schemes are derived.