SUMMARY The goal of this project is to rapidly construct an order‐by‐order level snapshot of financial markets with nanosecond resolution time stamps. We are particularly interested in understanding the impact of high‐frequency traders on the security, stability, and fairness of these markets. In this paper, we describe our computational approach, the optimizations that were applied to improve the performance of the software by a factor of more than 125×, and the new capabilities that can be enabled using a combination of fast algorithms and XSEDE resources. Copyright © 2014 John Wiley & Sons, Ltd.

Due to the low peak-to-mean envelope power ratio (PMEPR) of Golay sequences together with their connection to generalized Reed-Muller codes, many authors have proposed using Golay sequences as codewords in orthogonal frequency-division multiplexing (OFDM). Golay sequences that unexpectedly share the same aperiodic autocorrelation function can be used to construct longer Golay sequences. We study the shared autocorrelation property of general sequences with the ultimate goal of using those results to find other low power sequences. In this paper, we provide several new constructions of families of pairs of sequences with the shared autocorrelation property that enable us to explain nearly all of the binary shared autocorrelation property for sequences of lengths up to 24.