On Koetter's algorithm and the computation of error values (Q1431617)

Sakata's generalization of the Berlekamp-Massey decoding algorithm has been used as the foundation for decoding algebraic geometry codes in, for example, \textit{S. Sakata}, \textit{H. E. Jensen} and \textit{T. Høholdt} [IEEE Trans. Inf. Theory 41, 1762--1768 (1995; Zbl 0847.94014)], \textit{C. Heegard} and \textit{K. Saints} [ibid. 41, 1733--1751 (1995; Zbl 0861.94031)], the author [ibid. 41, 1709--1719 (1995; Zbl 0863.94028)], and \textit{R. Kötter} [ibid. 44, 1353--1368 (1998; Zbl 0994.94037)]. Here, the author, using some of the ideas in an earlier paper [J. Pure Appl. Algebra 169, 295--320 (2002; Zbl 1009.94015)], shows that Koetter's algorithm, which computes error locators, may also be used to compute error evaluator polynomials. In addition, it is shown that the update polynomials and the derivatives of the locators in Koetter's algorithm may be used to compute error values, making it unnecessary to compute error evaluator polynomials.