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Nonlinearity is one of the most challenging combinatorial property in the domain of Boolean function research. Obtaining nonlinearity greater than the bent concatenation bound for odd number of variables continues to be one of the most sought after combinatorial research problems. The pioneering result in this direction has been discovered by Patterson and Wiedemann in 1983 (IEEE-IT), which considered Boolean functions on 5×3 = 15 variables that are invariant under the actions of the cyclic group GF(25 ) ∗ · GF(23 ) ∗ as well as the group of Frobenius authomorphisms. Some of these Boolean functions posses nonlinearity greater than the bent concatenation bound. The next possible option for exploring such functions is on 7×3 = 21 variables. However, obtaining such functions remained elusive for more than three decades even after substantial efforts as evident in the literature. In this presentation, we exploit combinatorial arguments together with heuristic search to demonstrate such functions for the first time. This is a joint work with Subhamoy Maitra. Next, if time permits, we will revisit the definition of the modified transparency order (Chakraborty et al., WCC 2015), which is a revised version of the transparency order (Emmanuel Prouff, FSE 2005) introduced to quantify the resistance of an S-box against differential power analysis.