Abstract: In an error-correcting apparatus for correcting errors included in reproduced data which are stored in a RAM, a syndrome generation circuit, a polynomial calculation circuit for calculating an error position polynomial and an error value polynomial, and a position calculation circuit for calculating an error position are operated in parallel. A divider section of the error-correcting apparatus has a divider for performing the division of highest-degree coefficients of two polynomials, a multiplier for multiplying the coefficient of the polynomial set in the divisor side of the divider by the output of the divider, and an adder for adding the output of the multiplier and the coefficient of the polynomial set in the dividend side of the divider. The divider section executes the division over a Galois field while sequentially shifting the contents of registers which store the coefficient data of the dividend polynomial.

Abstract: In a magnetic recording/playback apparatus for recording and playing back a digital video signal on a helical track of a magnetic tape using two or more rotary heads, the playback image at the time of high-speed playback is improved by setting the tape travel speed at the time of high-speed playback at an even multiple of a normal playback speed. Further a tracking phase is offset by one half the track pitch with respect to the tracking during normal speed playback. Alternatively, essential information of the information having been high-efficiency coded is recorded in the central part, and near the ends of the tracks, while high-precision information is recorded in intermediate parts intermediate between the central part and the parts near the ends. Still alternatively, the video data of one of the consecutive fields is recorded in the central part of the tracks and the video data of the other of the consecutive fields is recorded near the ends of the tracks.

Abstract: Specified modular arithmetic is applied to input digital data to divide the input data into two main codes and a subcode. Otherwise, input digital data is divided into two pieces of digital data according to a specified rule. The digital data is divided so that the original input digital data can be completely restored if the two main codes and the subcode or both of the divided data are used, and the original input digital data can be nearly correctly restored even when one of the main codes or one of the divided data is used.