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This research work develops a general theoretical framework for analyzing the linear complexity of periodic sequences over finite fields. It characterizes the linear complexity of sequences with period 𝑁 N in terms of the roots of unity and their multiplicities, introducing Hasse derivatives to quantify these multiplicities. The authors also define a generalized discrete Fourier transform applicable to sequences of arbitrary length over fields with characteristic 𝑝 p. The theory is used to provide a proof of the Games–Chan algorithm for computing the linear complexity of binary sequences and extends the method to more general periodic sequences over finite fields.

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245: $a: Linear Complexity of Periodic Sequences: A General Theory
245: $b:
082: $a:
100: $a: James L. Massey & Shirlei Serconek
650: $a: Cryptography
250: $a:
440: $v:
250: $b: Springer Verlag
250: $c: 1998
020: $a:
300: $a: 14