Multidimensional Latin Bitrade

Original · EN

A subset S of k-ary n-dimensional hypercube is called latin bitrade if |S∩ F|∈{0,2} for each 1-face F. We find all admissible small (less than 2ⁿ⁺¹) cardinalities of latin bitrades. A subset M of k-ary n-dimensional hypercube is called t-fold MDS code if |M∩ F|=t for each 1-face F. Symmetric difference of two 1-fold MDS codes is always a latin bitrade. Symmetric difference of two t-fold MDS codes may also be a latin bitrade. In this case we say that this latin bitrade embedded into t-fold MDS code. The intersection of t-fold MDS code and a latin bitrade embedded into it is called a component of the code. We study the questions of embedding of latin bitrades into t-fold MDS and admissible cardinalities of the component of t-fold MDS. Keywords: MDS code, latin bitrade, component.