A Method to Extend Euclid's Algorithm to N Dimension

This paper shows that the equivalence relation between Berlekamp-Massey's algorithm and Euclid's algorithm extends to N dimensions. Using the extended equivalence relation, this paper proposes N-dimensional Euclid's algorithms corresponding to N-dimensional Berlekamp-Massey's algorithms. This paper shows that the proposed algorithms are suitable for parallel processing, which is difficult for Berlekamp-Massey's algorithms, to find a minimal set of polynomials capable of generating a given finite N-dimensional array. Therefore N-dimensional Euclid's algorithms can realize high-speed decoding of algebraic geometry codes using parallel processing.