Primitive linear recurring sequences over rings are important in modern communication technology, and character sums of such sequences are used to analyze their statistical properties. We obtain a new upper bound for the character sum of primitive sequences of order n over the residue ring modulo a square-free odd integer m, and thereby improve previously known bound mn/2.

In Long-Term Evolution (LTE)-Advanced, an important goal in addition to achieving high-speed, high-capacity communications is throughput enhancement for cell-edge users. One solution is to relay radio transmissions between an eNode B and user equipment (UE). Relays are expected to extend the coverage to the cell boundary and coverage hole areas, and are expected to reduce network costs. It was agreed that in Release 10 LTE, a Layer-3 (L3) relay, which achieves self-backhauling of radio signals between an eNode B and a UE in Layer 3 should be standardized. Meanwhile, a Layer-1 (L1) relay, which amplifies and forwards received radio frequency signals, has already found widespread use in second-generation and third-generation mobile communication systems. This paper investigates the downlink system level performance for L3 and L1 relays with orthogonal frequency division multiple access (OFDMA) in LTE-Advanced. Various practical factors are taken into account in the evaluations such as the processing delay and upper bound of the amplifier gain of the L1 relay, capacity limitation of the backhaul channels, and empty buffer status at the L3 relay. We also propose and investigate a downlink backhaul link (radio link between the eNode B and L3 relay node) scheduling method for the in-band half-duplex L3 relay. In the proposed scheduling method, radio resources from an eNode B to an L3 relay node and macro UE are multiplexed in the same backhaul subframe considering the number of relay UEs and macro UEs, and the channel quality of the backhaul link to the L3 relay and the access link to the macro UE. Based on system-level simulations, we clarify the system impact of several conditions for the relay such as the number of relay nodes and the number of backhaul (radio link between eNode B and L3 relay) subframes, the distance between the eNode B and relay, and show the throughput performance gain of the L3 relay compared to the L1 relay. We also clarify that the cell-edge UE throughput performance is increased by approximately 10% by applying the proposed scheduling method due to more efficient and fair resource allocation to the L3 relay and macro UEs.

MICKEY-family ciphers are lightweight cryptographic primitives and include a register R determined by two related maximal-period linear transformations. Provided that primitivity is efficiently decided in finite fields, it is shown by quantitative analysis that potential parameters for R can be found in probabilistic polynomial time.