The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes.>

Linear codes are considered. A code is characterized by the length n, the dimension k, and the minimum distance d. An (n,k,d) code over the finite field GF(q) is said to be maximum distance separable (MDS) if d=n-k+1. A. Krishna and D.V. Sarwate (1990) investigated the existence of pseudo-cyclic MDS codes over GF(q) of length n, where n divides q-1 or q+1. It is shown that the pseudo-cyclic MDS codes constructed by Krishna and Sarwate are generalised Reed-Solomon codes. Pseudo-cyclic codes are studied over GF(q), where n and q=p/sup h/ are not relatively prime. It is proven that pseudo-cyclic (n,k) MDS codes modulo (x/sup n/-a) over GF(q) exist, if and only if n= p. Furthermore, any pseudo-cyclic (p,k) code modulo (x/sup p/-a) over GF(q) turns out to be MDS and generalized Reed-Solomon. It is explicitly proven that some classes of pseudo-cyclic (n,k) MDS codes over GF(q) are generalized Reed-Solomon codes. Furthermore, pseudo-cyclic (q+1,4) MDS codes over GF(q), q even, are completely classified.>