Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing and Counting Even-Variable Symmetric Boolean Functions with
  Algebraic Immunity not Less Than $d$   In this paper, we explicitly construct a large class of symmetric Boolean
functions on $2k$ variables with algebraic immunity not less than $d$, where
integer $k$ is given arbitrarily and $d$ is a given suffix of $k$ in binary
representation. If let $d = k$, our constructed functions achieve the maximum
algebraic immunity. Remarkably, $2^{\lfloor \log_2{k} \rfloor + 2}$ symmetric
Boolean functions on $2k$ variables with maximum algebraic immunity are
constructed, which is much more than the previous constructions. Based on our
construction, a lower bound of symmetric Boolean functions with algebraic
immunity not less than $d$ is derived, which is $2^{\lfloor \log_2{d} \rfloor +
2(k-d+1)}$. As far as we know, this is the first lower bound of this kind.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics