On Bilinear Quasigroups of Order 2^n

The standard representation of a quasigroup of order m uses m2 bits. In this paper, it is introduced a new way for representation of a class of quasigroups of order 2n, that reduces the number of bits required for the representation. The focus is placed on a class of quasigroups that can be represented as a linear combination of the operands, which requires ln(m) bits for storage a quasigroup of order m. Moreover, some characteristics about the parameters, i.e. matrices, that are used for defining such quasigroups are given. This model for presentation of quasigroups can be easily used for further testing of their coding and cryptographic features