Since 1968, when the Golomb–Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb–Welch conjecture. Further, new results on Golomb–Welch con...

We study the nonlinearity of Exponential Welch Costas functions using the Fourier transform on Zn. Exponential Welch Costas functions are bijections from Zp−1 to Zp−1 defined using the exponential function of Zp, where p is an odd prime. Their linearity properties were recently studied by Drakakis, Requena, and McGuire, who conjectured that the absolute values of the Fourier coefficients of an ...

Abstract This survey presents the rich history of Welch-Gong (WG) Stream cipher family. It has been a long journey that lead WG stream ciphers to become practical. The evolutionary path is combination mathematical endeavour and engineering striving transfer pure functions practical encryption algorithms for various applications. began as pioneering work on transformation sequences with 2-level ...

MOTIVATION In searching for differentially expressed (DE) genes in microarray data, we often observe a fraction of the genes to have unequal variability between groups. This is not an issue in large samples, where a valid test exists that uses individual variances separately. The problem arises in the small-sample setting, where the approximately valid Welch test lacks sensitivity, while the mo...

Exploiting the empirical observation that the probability of k fixed points in a Welch Costas permutation is approximately the same as in a random permutation of the same order, we propose a stochastic model for the most probable maximal number of fixed points in a Welch Costas permutation.

A geometric perspective is used to derive the entire family of Welch bounds. This perspective unifies a number of observations that have been made regarding tightness of the bounds and their connections to symmetric k-tensors, tight frames, homogeneous polynomials, and tdesigns. Index Terms – Frames, Grammian, Homogeneous polynomials, Symmetric tensors, t-designs, Welch bounds

We propose a new method for the estimation of parameters of hidden diffusion processes. Based on parametrization of the transition matrix, the Baum-Welch algorithm is improved. The algorithm is compared to the particle filter in application to the noisy periodic systems. It is shown that the modified Baum-Welch algorithm is capable of estimating the system parameters with better accuracy than p...