Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Sequences with a Perfect Linear Complexity Profile   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.

37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
18
The categories of this paper are: econ
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an