Multidimensional Latin Bitrade
Vladimir N. Potapov

TL;DR
This paper characterizes small latin bitrades within hypercubes, explores their relation to t-fold MDS codes, and investigates embedding properties and component sizes, advancing combinatorial design theory.
Contribution
It provides a complete classification of small latin bitrades and analyzes their embedding into t-fold MDS codes, introducing new structural insights.
Findings
All admissible small cardinalities of latin bitrades are identified.
Symmetric difference of two 1-fold MDS codes always forms a latin bitrade.
Conditions for embedding latin bitrades into t-fold MDS codes are established.
Abstract
A subset of -ary -dimensional hypercube is called latin bitrade if for each 1-face . We find all admissible small (less than ) cardinalities of latin bitrades. A subset of -ary -dimensional hypercube is called -fold MDS code if for each 1-face . Symmetric difference of two 1-fold MDS codes is always a latin bitrade. Symmetric difference of two -fold MDS codes may also be a latin bitrade. In this case we say that this latin bitrade embedded into -fold MDS code. The intersection of -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 -fold MDS and admissible cardinalities of the component of -fold MDS. Keywords: MDS code, latin bitrade, component.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Interconnection Networks and Systems
