The Berlekamp-Massey algorithm is an algorithm for determining the linear complexity of a finite sequence and the feedback polynomial of a linear feedback shift register (LFSR) of minimal length which generates this sequence. This algorithm is due to Massey, who showed that the iterative algorithm proposed in 1967 by Berlekamp for decoding BCH codes (see cyclic codes) can be used for finding the shortest LFSR that generates a given sequence.
For a given sequence s n of length n, the Berlekamp-Massey algorithm performs n iterations. The tth iteration determines an LFSR of minimal length, which generates the first t digits of s n. The algorithm can be described as follows.
This is a preview of subscription content, log in via an institution to check access.
References
Berlekamp, E.R. (1967). Algebraic Coding Theory. McGraw-Hill, New York.
Dornstetter, J.-L. (1987). “On the equivalence between Berlekamp's and Euclid's algorithms.” IEEE Transactions on Information Theory, 33, 428–431.
Massey, J.L. (1969). “Shift-register synthesis and BCH decoding.” IEEE Transactions on Information Theory, 15, 122–127.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 International Federation for Information Processing
About this entry
Cite this entry
Canteaut, A. (2005). Berlekamp-Massey algorithm. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_24
Download citation
DOI: https://doi.org/10.1007/0-387-23483-7_24
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23473-1
Online ISBN: 978-0-387-23483-0
eBook Packages: Computer ScienceReference Module Computer Science and Engineering