In this paper, we construct a new fast transform built on a similar structure with Fast Fourier Transform (FFT), which accelerates calculating polynomials modulo a specific group of moduli. The new transform can be expanded into polynomial remainder codes with lower time complexities. Besides, applying the fast transform in weighted threshold secret sharing with threshold t among N participants requires$O(Nt)$field operations, that improves the prior result$O(Nt\log ^{2} t\log \log t)$. In addition, the decoding algorithm requires$O(t\log ^{2}\log \log t)$field operations, that improves the prior result$O(Nt\log ^{2} t\log \log t)$.

Inversion encoding is an encoding technique used to encode bus transmissions in low-power systems. It is typically utilized to save energy by decreasing the number of transitions on the bus. When the data is transmitted into the bus, the conventional method adds an INV signal to indicate whether the data is inverted. The method reduces the average and the maximal number of transitions and results in the reduction of average and peak power dissipation. However, the method still has room for improvement. We propose an efficient inversion encoding method by adding$k$INV signals on bus transmission to achieve a smaller average number of transitions, which is supported by the results of the numerical calculations.

In this paper, we study the straggler mitigation via coded computing in distributed computations. In particular, we consider the coded matrix-vector multiplication where the matrix is sparse and coding may break the sparsity of the matrix. We construct a class of sparse universal decodable matrices (UDMs) for coded computing. In simulations, it shows that the proposed code possesses better sparsity than other schemes with randomly generated sparse matrices. Besides, the proposed code performs well in numerical stability.

Secret sharing is the method to share secrets among a group of shares, and the secret can be reconstructed if one obtains a predefined number of shares. The polynomial secret sharing is usually constructed over a field. In this letter, a novel polynomial secret sharing over a ring is proposed. In particular, by choosing a certain ring, the fast Fourier transform can be applied on the encoding of secret sharing. The analysis shows that the proposed secret sharing scheme requires O(N log2N) Boolean operations per secret bit, which improves the prior result O(8log* NN log2N) Boolean operations per secret bit. The simulation shows that the proposed scheme is in average four times faster than the conventional approach.