Method and device for decoding the algebraic-geometric codes at a point, comprises the construction of a sequence of syndromes matrices ending with a zero row elements matrix

摘要

The method for decoding an algebraic-geometric code at a point of dimension k and length n, in order to identify the position of errors in a received word, defines the syndromes matrix S of dimensions (n-k)-(n-k) whose elements Sij of each row i are computed for j between 1 and w(i), where the boundary w is a decreasing function, on the basis of syndrome s of the received word. The method comprises the construction of matrices Su for successive values of u by beginning with S1 = S, where each matrix Su for u greater than 1 is obtained from the matrix Su-1 by permutating the columns of matrix Su-1 and then by linear manipulations on the row of index u of the obtained matrix. The construction of matrices is terminated when either the matrix elements of row u and column j vanish (Suuj=0) for all j between 1 and w(u), or if there exist an integer uasterisk not greater than u-1 such that the matrix elements of row uasterisk and column j vanish (Suasteriskuasterisk+j=0) for all j between 1 and w(u). The final step is either the step numbered u = lambda, if an integer lambda is determined such that the matrix elements of row lambda and column j vanish (Sapproximatelylapproximatelylj=0) for all j between 1 and w(lambda), or the step numbered u=(lambda-1), if an integer lambda and an integer uasterisk, which is lesser than lambda, are determined so that the matrix elements of row uasterisk and column j vanish (Suasteriskuasteriskj=0) for all j between 1 and w(lambda). The number of rows of each matrix Su is truncated to umax, where umax is the smallest integer i for which w(i) is lesser than i. The number of columns of each matrix Su is truncated to w(u). The number of columns of each matrix Su is truncated to w(muD) for u between 1 and the Duursma minimum muD, and to w(u) for u greater than muD. A device (claimed) implements the method (claimed). A decoder (claimed) comprises at lesat one device as claimed for error correction, and at least one unit for the redundancy suppression. An apparatus (claimed) for the reception of coded digital signals comprises the decoder and means for demodulating the coded digital signals. An information system (claimed) comprises the decoder and at least one hard disc, and means for reading the hard disc. A storage means (claimed) for data comprises the instructions of information program code for executing the steps of the method. A computer program (claimed) comprises instructions required of a programmable data processing device to implement the method.