Related papers: An infinite class of quantum codes derived from du…
We construct qubit stabilizer codes with parameters $[[81, 0, 20]]$ and $[[94, 0, 22]]$ for the first time. We use symplectic self-dual additive codes over $\mathbb{F}_4$ built by modifying the adjacency matrices of suitable metacirculant…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its…
We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the…
We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…
We study constacyclic codes, of length $np^s$ and $2np^s$, that are generated by the polynomials $(x^n + \gamma)^{\ell}$ and $(x^n - \xi)^i(x^n + \xi)^j$\ respectively, where $x^n + \gamma$, $x^n - \xi$ and $x^n + \xi$ are irreducible over…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
This paper provides a comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes of length $4p^{\varsigma}$ over the finite field $\mathbb{F}_{p^m}$, where $p$ is an odd prime number. Furthermore, it introduces…
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…
New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters $[[127,63, \geq 12]]_2$ and $[[63,45, \geq 6]]_4$ that are records. These codes are…
A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for…
This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the…
In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…