An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata, focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter.

翻译：在对用于加密和编码理论的布尔功能的研究中,一个有趣的线索是对二次构造的研究:鉴于已知的功能具有良好的加密剖面,目的是将其扩大到具有类似属性的(通常较大的)功能。在这项工作中,我们继续调查基于细胞自动成像的二级构造,重点是弯曲和半成像功能的类别。我们证明我们的建筑保留了当地规则的代数度,我们缩小了对二次构造的注意,在通过进化战略进行详尽的组合搜索和超速优化的基础上进行了若干次实验。最后,我们将所获得的结果分类为变异等,指出我们的CA-XOR建筑能够成功地扩展到CA直径的等同类数量迅速增长。