On quasi‐orthogonal cocycles.

Abstract: We introduce the notion of quasi‐orthogonal cocycle. This is motivated in part by the maximal determinant problem for square { ± 1 }‐matrices of size congruent to 2 modulo 4. Quasi‐orthogonal cocycles are analogous to the orthogonal cocycles of algebraic design theory. Equivalences with new and known combinatorial objects afforded by this analogy, such as quasi‐Hadamard groups, relative quasi‐difference sets, and certain partially balanced incomplete block designs, are proved. [ABSTRACT FROM AUTHOR]