Abstract: The magnetic code may include a run of b spoiled bits in a position that is locatable. The system consists in adding a check structure of k bits to the m-bit message in such a manner that the resulting n-bit word n=m+k is a cyclic redundancy code word generated by a generator polynomial G(x) of degree k that divides x.sup.n -1 without remainder in modulo-2 algebra. On reading, the system locates a packet of spoilt bits by detecting magnetic spoiling of the track which should normally be in the form of magnets of length l.sub.1 =l.+-.l/2 and l.sub.2 =2l.+-.l/2, with there being no runs of an odd number of successive magnets of length l.sub.1, given the bi-phase code used. A detected error is corrected by applying the relationship G(x) to the message as read after circular permutation has been applied thereto to move the missing bits to the end of the message.