相关论文: Primitive Quantum BCH Codes over Finite Fields
In this paper, we investigate the first few largest coset leaders modulo $\frac{q^m+1}{\lambda}$ where $\lambda\mid q+1$ and $q$ is an odd prime power, and give the dimensions of some LCD BCH codes of length $\frac{q^m+1}{\lambda}$ with…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking…
Determining the exact decoding error probability of linear block codes is an interesting problem. For binary BCH codes, McEliece derived methods to estimate the error probability of a simple bounded distance decoding (BDD) for BCH codes.…
In a paper from 2015, Ding et al. (IEEE Trans. IT, May 2015) conjectured that for odd $m$, the minimum distance of the binary BCH code of length $2^m-1$ and designed distance $2^{m-2}+1$ is equal to the Bose distance calculated in the same…
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…
A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a…
We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual code by means of unitary matrices, where some of them generalize the quadratic double circulant constructions.…
We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Let $\mathbb{F}_q$ be the finite field of $q$ elements, where $q=p^{m}$ with $p$ being a prime number and $m$ being a positive integer. Let $\mathcal{C}_{(q, n, \delta, h)}$ be a class of BCH codes of length $n$ and designed $\delta$. A…
Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further,…
In recent years, polar codes have been considered for communication systems that require high re-liability and ultra-low latency, such as sixth generation (6G) wireless communications. This paper presents simulation results showing that…
Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined. In this paper we present new values of…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum…
The setting of projective systems can be used to study the parameters of a projective linear code $\mathcal{C}$. This can be done by considering the intersections of the point set $\Omega$ defined by the columns of a generating matrix for…
The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…