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    • 13. 发明授权
    • Error correcting system for correcting two or three simultaneous errors
in a code
    • 错误纠正系统,用于纠正代码中的两个或三个同时发生的错误
    • US4468769A
    • 1984-08-28
    • US349319
    • 1982-02-16
    • Keiichiro Koga
    • Keiichiro Koga
    • H03M13/15G06F11/10
    • H03M13/15
    • An improved two or three error correcting system for BCH code (Bose, Chaudhuri, Hocquenghem code) has been found. In case of a two error correction system, a first syndrome A.sub.1 and a second syndrome A.sub.2 are obtained from a reception code C'=(a.sub.1 ', a.sub.2 ', . . . , a.sub.n '): ##EQU1## Then, S.sub.1 =A.sub.1 +.alpha..sup.n-t, and S.sub.2 =A.sub.2 +.alpha..sup.3(n-t) are obtained, for every value of t, where n is a code length, t is an integer equal to or less than n, and .alpha. is a primitive element of a Galois field. When A.sub.1 .noteq.0, a t'th bit a.sub.t ' is corrected by inverting the same on the condition that the t'th bit of S.sub.2 is equal to the t'th bit of S.sub.1.sup.3. When A.sub.1 =0, it is clear that no error exists, and no correction is performed. In case of a three error correction system, a third syndrome ##EQU2## and S.sub.3 =A.sub.3 +.alpha..sup.5(n-t) are obtained further for every value of t, and a correction is performed by inverting the t'th bit according to the value of EL(t)=S.sub.1.sup.6 +S.sub.2.sup.2 +S.sub.1.sup.3 S.sub.2 +S.sub.1 S.sub.3 when A.sub.1.sup.3 +A.sub.2 .noteq.0, or the value of S.sub.1 when A.sub.1.sup.3 +A.sub.2 =0. The structure of the present system is simple since said values S.sub.2, S.sub.3 and EL(t) are obtained merely by a ROM table and an exclusive-OR circuit.
    • 已经发现了用于BCH码(Bose,Chaudhuri,Hocquenghem码)的改进的两个或三个纠错系统。 在两个纠错系统的情况下,从接收码C'=(a1',a2',...,an')获得第一综合征A1和第二综合征A2:然后,S1 = A1 + 对于t的每个值,获得αnt,并且S2 = A2 +α3(nt),其中n是码长,t是等于或小于n的整数,并且α是伽罗瓦域的原始元素。 当A1 NOTEQUAL 0时,在第t个第s位等于S13的第t位的条件下,通过将其反相来校正't'的第t位。 当A1 = 0时,显然没有错误,不进行校正。 在三个错误校正系统的情况下,对于t的每个值进一步获得第三综合征和S3 = A3 +α5(nt),并且通过根据t的值反转第t位来执行校正 当A13 + A2为等于0时,EL(t)= S16 + S22 + S13S2 + S1S3,或者A13 + A2 = 0时的S1的值。 由于所述值S2,S3和EL(t)仅由ROM表和异或电路获得,所以本系统的结构是简单的。