Representing X-Code Using Latin Squares

X-code is an important 2-erasure correcting vertical array code. In this paper, we present a combinatorial representation for X-code. It is based on graph representation of binary linear/array codes. We represent X-code by Cayley tables of the cyclic groups of prime order - a special column-Hamiltonian Latin squares (CHLS). This representation is helpful to comprehend X-code´s 2-erasure correcting ability. We also show the inner relationship between X-code and the liberation codes though the former is a vertical code and the latter is a horizontal code. A possible way to construct the 2-erasure vertical codes like X-code using common CHLS is also proposed.