On Sequences with a Perfect Linear Complexity Profile

Details On Sequences with a Perfect Linear Complexity Profile On Sequences with a Perfect Linear Complexity Profile

2011-08-22

arxiv.org/abs/1108.4224v2

Computer Science

Information Theory

19 pages, 3 tables

Scientific paper

We derive B\'ezout identities for the minimal polynomials of a finite sequence and use them to prove a theorem of Wang and Massey on binary sequences with a perfect linear complexity profile. We give a new proof of Rueppel's conjecture and simplify Dai's original proof. We obtain short proofs of results of Niederreiter relating the linear complexity of a sequence s and K(s), which was defined using continued fractions. We give an upper bound for the sum of the linear complexities of any sequence. This bound is tight for sequences with a perfect linear complexity profile and we apply it to characterise these sequences in two new ways.

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