In this paper, we present PDHLatin - a new class of 2-erasure horizontal codes with dependent parity symbols based on column-hamiltonian Latin squares (CHLS). We prove that PDHLatin codes are MDS codes. We also present a new class of 2-erasure parity independent mixed codes based on CHLS - PIMLatin. We show that the performance of the new codes is comparable to or better than other codes of this kind. They have perfect parameter flexibility and structure variety that benefit performance. We also discuss code shortening technologies that can improve parameter flexibility, structure variety and reliability. Borrowing ideas from vertical shortening, we develop a 2-erasure array code construction method using non-hamiltonian Latin squares.