Abstract: A data storage system has error detecting and correcting system having three error codes. The data are arranged logically as a three-dimensional array consisting of a plurality of logically rectangular blocks of data. Each block of data has columns and rows of data. A first error code that corrects errors creates a first redundancy in each of the columns. A like-positioned block row of data in each of the blocks constitutes an array row of data. The array rows are grouped into sets of array rows, the number of array rows in each set vary inversely with a number of tracks of a record medium that concurrently receive the data for recording. Each set of data are recorded serially by bit in respective tracks of the tape record medium. Before recording, the block rows are logically rotated (end-around shifted) within each of the array rows.