Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Design of Quantum Stabilizer Codes From Quadratic Residues Sets   We propose two types, namely Type-I and Type-II, quantum stabilizer codes
using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The
proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$.
They are constructed based on multi-weight circulant matrix generated from
idempotent polynomial, which is obtained from a quadratic residue set. The
proposed Type-II stabilizer codes are of quasi-cyclic (QC) structure and code
length $N=pk$, where $k$ is the size of a quadratic residue set. They are
constructed based on structured sparse-graphs codes derived from proto-matrix
and circulant permutation matrix. With the proposed methods, we design rich
classes of cyclic and quasi-cyclic quantum stabilizer codes with variable code
length. We show how the commutative constraint (also referred to as the
Symplectic Inner Product constraint) for quantum codes can be satisfied for
each proposed construction method. We also analyze both the dimension and
distance for Type-I stabilizer codes and the dimension of Type-II stabilizer
codes. For the cyclic quantum stabilizer codes, we show that they meet the
existing distance bounds in literature.

7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th