Encounters with the Berlekamp-Massey Algorithm

In 1969, J. Massey published a now-famous paper showing, among other things, that an iterative algorithm introduced by Berlekamp for decoding BCH codes also solved the problem of finding a shortest-length feedback shift register circuit for generating a given finite sequence of digits. This nice physical interpretation opened the door to connections with many other problems, including the minimal partial realization problems of linear system theory, Pade approximations and continued fractions, the fast algorithms of Levinson and Schur for Toeplitz matrices, inverse scattering, VLSI implementations, etc. This paper is an informal account of some of the different contexts in which the Berlekamp-Massey algorithm have been encountered in the work of the author and his students.

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