The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over Mn×s(F2[u,v]/) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over Mn×s(F2[u,v]/) are obtained. Finally, we give two examples to illustrate the results we obtained.

A simple and novel multiple-symbol differential detection (MSDD) scheme is proposed for IEEE 802.15.4 binary phase shift keying (BPSK) receivers. The detection is initiated by estimating and compensating the carrier frequency offset (CFO) effect in the chip sample of interest. With these new statistics, the decisions are jointly made by allowing the observation window length to be longer than two bit intervals. Simulation results demonstrate that detection reliability of the IEEE 802.15.4 BPSK receivers is significantly improved. Namely, at packet error rate (PER) of 1×10-3, the signal-to-noise ratio (SNR) gap between ideal coherent detection (perfect carrier reference phase and no CFO) with differential decoding and conventional optimal single differential coherent detection (SDCD) is filled by 2.1dB when the observation window length is set to 6bit intervals. Then, the benefit that less energy consumed by retransmissions is successfully achieved.

Due to the rapid development of different processors, e.g., x86 and Sunway, software porting between different platforms is becoming more frequent. However, the migrated software's execution efficiency on the target platform is different from that of the source platform, and most of the previous studies have investigated the improvement of the efficiency from the hardware perspective. To the best of our knowledge, this is the first paper to exclusively focus on studying what software factors can result in performance change after software migration. To perform our study, we used SonarQube to detect and measure five software factors, namely Duplicated Lines (DL), Code Smells Density (CSD), Big Functions (BF), Cyclomatic Complexity (CC), and Complex Functions (CF), from 13 selected projects of SPEC CPU2006 benchmark suite. Then, we measured the change of software performance by calculating the acceleration ratio of execution time before (x86) and after (Sunway) software migration. Finally, we performed a multiple linear regression model to analyze the relationship between the software performance change and the software factors. The results indicate that the performance change of software migration from the x86 platform to the Sunway platform is mainly affected by three software factors, i.e., Code Smell Density (CSD), Cyclomatic Complexity (CC), and Complex Functions (CF). The findings can benefit both researchers and practitioners.

Let $R$ = $mathbb{F}_{p}+umathbb{F}_{p}+vmathbb{F}_{p}+uvmathbb{F}_{p}$, where u2=u, v2 and uv=vu. A relation between the support weight distribution of a linear code $mathscr{C}$ of type p4k over R and its dual code $mathscr{C}^{ot}$ is established.