Related papers: Quasi-Cyclic Constructions of Quantum Codes
Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent…
We relate the semiclassical limit of the quantum Yang-Mills partition function on a compact oriented surface to the symplectic volume of the moduli space of flat connections, by using an explicit expression for the symplectic form. This…
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…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
It is proved that the entire multi-parameter (small-)quantum groups of symmetrizable Kac-Moody algebras can be realized as certain subquotients of the cotensor Hopf algebras. This is an axiomatic construction. Hopf 2-cocycle deformations…
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear complementary pairs of quasi-cyclic and quasi-twisted codes…
Binary self-dual cyclic codes have been studied since the classical work of Sloane and Thompson published in IEEE Trans. Inf. Theory, vol. 29, 1983. Twenty five years later, an infinite family of binary self-dual cyclic codes with lengths…
There have been significant recent advances in constructing theoretical and practical quantum error correcting codes that function well as quantum memories; however, performing fault-tolerant logical gates on these codes is less studied,…
We study the algebraic geometry of a family of evaluation codes from plane smooth curves defined over any field. In particular, we provide a cohomological characterization of their dual minimum distance. After having discussed some general…
We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.
In this paper we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through…
We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational…
Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of…
Let $\mathbb{F}_q$ be a finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(\gamma,\Delta)$-cyclic codes over a class of finite non-chain commutative rings…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
In this paper we study the structure of $\theta$-cyclic codes over the ring $B_k$ including its connection to quasi-$\tilde{\theta}$-cyclic codes over finite field $\mathbb{F}_{p^r}$ and skew polynomial rings over $B_k.$ We also…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
By incorporating the concept of locality into quantum information theory, quantum locally recoverable codes (qLRCs) have been proposed, motivated by their potential applications in large-scale quantum data storage and their relevance to…