@article {IOPORT.05717004, author = {Dimitrova, Vesna and Markovski, Smile and Mileva, Aleksandra}, title = {Periodic quasigroup string transformations.}, year = {2009}, journal = {Quasigroups and Related Systems}, volume = {17}, number = {2}, issn = {1561-2848}, pages = {191-204}, publisher = {Institute of Mathematics, Chi\c sin\u au; Higher College of Engineering in Legnica, Legnica}, abstract = {Summary: Given a finite quasigroup \$(Q,*)\$, quasigroup string transformations \$e_l\$ and \$d_l\$ over the strings of elements from \$Q\$ are defined as follows. \$e_l(a_1a_2\dots a_n)=b_1b_2\dots b_n\$ if and only if \$b_i=b_{i-1}*a_i\$ and \$d_l(a_1a_2\dots a_n) =b_1b_2\dots b_n\$ if and only if \$b_i = a_{i-1}*a_i\$, for each \$i=1,2,...,n\$, where \$l=a_0=b_0\$ is a fixed element of \$Q\$. A quasigroup string \$e\$- or \$d\$-transformation \$t\$ is periodical if for some periodic string we have \$t(a_1a_2\dots a_ka_1a_2\dots a_k\dots a_1a_2\dots a_k)= a_1a_2\dots a_ka_1a_2\dots a_k\dots a_1a_2\dots a_k\$. The quasigroup string transformations are used in many fields, like: cryptography for designing different cryptographic tools, coding theory for designing error-detecting and error-correcting codes, etc. The properties of the quasigroup string transformations depend on the used quasigroups, and some quasigroups are suitable for cryptographic designs, while some others are suitable for code designs. We give a characterization of the quasigroups producing periodic string transformations, and for that aim quasigroups with period \$k\$ are defined. One can use this characterization for choosing suitable quasigroups in some applications.}, identifier = {05717004}, }