The Application of q-ary Codes for the Correction of Single Peak-Shifts, Deletions and Insertions of Zeros

We construct q-ary block codes that allow correction of specific types of double errors. These codes can be used as codes for correction of peak-shifts, deletions and insertions of zeros in (d,k)-sequences applied in magnetic recording. For single peak-shifts over t /spl les/ (k-d)/2 positions left or right, the codes have dimension N=q/sup r/, K=q/sup r/-(r+1), q=k-d+1. An additional condition on the structure of the code gives transparent block codes which are used to control the maximum binary length of the code words. Encoding and decoding are done by simple algorithms without using look-up tables, enumeration or denumeration procedures and therefore the code length may be large. The rate of the overall encoding approaches (2log/sub 2/(k-d+1))/( k+d+2) for large code word lengths.