Diagonals of 2D-abelian codes

It is well known that the rows and the columns of a 2D-abelian (2D-cyclic) code of area n×m can be considered as codewords of some cyclic codes. It is shown that if m divide n or if n divide m, then the diagonals of the codewords can be also considered as codewords of some cyclic codes. This result can be used for the decoding of product codes constructed from two cyclic codes