| 摘要 |
A decoder suitable for use in a digital communications system utilizing an RS(n', k') code modified from an RS(n, k) code receives n'-symbol vectors each including k' message symbols and r'=n'-k' parity symbols and decodes the n'-symbol vectors to correct errors therein, wherein n, k, n', and k' are integers, and k'<n'<n, k'<k<n, and wherein the decoder stores therein one erasure locator polynomial sigma<SUB>0</SUB>(x). The decoder includes a syndrome calculator for receiving the n'-symbol vectors and for calculating syndromes of each n'-symbol vector, wherein the i-th syndrome S<SUB>i </SUB>of one n'-symbol vector R', (r<SUB>n'-1</SUB>, r<SUB>n'-2</SUB>, . . . , r<SUB>0</SUB>), is S<SUB>i</SUB>=R<SUB>s</SUB>(alpha<SUP>i+1</SUP>) for i=0, 1, . . . , n-k-1, wherein R<SUB>s</SUB>(x)=r<SUB>n'-1</SUB>x<SUP>n'-1</SUP>+r<SUB>n'-2</SUB>x<SUP>n'-2</SUP>+ . . . +r<SUB>0</SUB>, and means for finding the locations and values of the errors in each n'-symbol vector using the syndromes thereof and the one erasure locator polynomial sigma<SUB>0</SUB>(x).
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