Cunsheng Ding
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View article: Some constructions of non-generalized Reed-Solomon MDS Codes
Some constructions of non-generalized Reed-Solomon MDS Codes Open
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs …
View article: Trusted Fake Audio Detection Based on Dirichlet Distribution
Trusted Fake Audio Detection Based on Dirichlet Distribution Open
With the continuous development of deep learning-based speech conversion and speech synthesis technologies, the cybersecurity problem posed by fake audio has become increasingly serious. Previously proposed models for defending against fak…
View article: Self-Dual Cyclic Codes with Square-Root-Like Lower Bounds on Their Minimum Distances
Self-Dual Cyclic Codes with Square-Root-Like Lower Bounds on Their Minimum Distances Open
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 …
View article: Two classes of constacyclic codes with a square-root-like lower bound
Two classes of constacyclic codes with a square-root-like lower bound Open
Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic str…
View article: Repeated-Root Cyclic Codes with Optimal Parameters or Best Parameters Known
Repeated-Root Cyclic Codes with Optimal Parameters or Best Parameters Known Open
Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes an…
View article: Cyclic and Negacyclic Sum-Rank Codes
Cyclic and Negacyclic Sum-Rank Codes Open
Sum-rank codes have known applications in the multishot network coding, the distributed storage and the construction of space-time codes. U. Mart\'ınez-Peñas introduced the cyclic-skew-cyclic sum-rank codes and proposed the BCH bound on th…
View article: More MDS codes of non-Reed-Solomon type
More MDS codes of non-Reed-Solomon type Open
MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and estab…
View article: Extended codes and deep holes of MDS codes
Extended codes and deep holes of MDS codes Open
For a given linear code $\C$ of length $n$ over $\gf(q)$ and a nonzero vector $\bu$ in $\gf(q)^n$, Sun, Ding and Chen defined an extended linear code $\overline{\C}(\bu)$ of $\C$, which is a generalisation of the classical extended code $\…
View article: The Extended Codes of Some Linear Codes
The Extended Codes of Some Linear Codes Open
The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended…
View article: The extended codes of a family of reversible MDS cyclic codes
The extended codes of a family of reversible MDS cyclic codes Open
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said …
View article: Four infinite families of ternary cyclic codes with a square-root-like lower bound
Four infinite families of ternary cyclic codes with a square-root-like lower bound Open
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in I…
View article: Several families of ternary negacyclic codes and their duals
Several families of ternary negacyclic codes and their duals Open
Constacyclic codes contain cyclic codes as a subclass and have nice algebraic structures. Constacyclic codes have theoretical importance, as they are connected to a number of areas of mathematics and outperform cyclic codes in several aspe…
View article: Five infinite families of binary cyclic codes and their related codes with good parameters
Five infinite families of binary cyclic codes and their related codes with good parameters Open
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in I…
View article: Editorial: Special issue on Boolean functions and their applications 2021
Editorial: Special issue on Boolean functions and their applications 2021 Open
View article: Two Classes of Constacyclic Codes with Variable Parameters
Two Classes of Constacyclic Codes with Variable Parameters Open
Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic code…
View article: Infinite families of cyclic and negacyclic codes supporting 3-designs
Infinite families of cyclic and negacyclic codes supporting 3-designs Open
Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been cons…
View article: Several Families of Irreducible Constacyclic and Cyclic Codes
Several Families of Irreducible Constacyclic and Cyclic Codes Open
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several famil…
View article: Two families of negacyclic BCH codes
Two families of negacyclic BCH codes Open
Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let $q$ be an odd prime power and $m$ be a positive integer. The object…
View article: On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and Their Consequences
On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and Their Consequences Open
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of\ncyclic codes that have found numerous applications in error correction and\nnotably in quantum information processing. A subclass of attractive BCH codes\nis the na…
View article: On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and their Consequences
On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and their Consequences Open
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. A subclass of attractive BCH codes is the narro…
View article: The subfield codes and subfield subcodes of a family of MDS codes
The subfield codes and subfield subcodes of a family of MDS codes Open
Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[2^m+1, 2u-1, 2^m-2u+3]$ MDS codes for $1 \leq u \leq 2^{m-1}$, which are cyclic, reversible and BCH c…
View article: The minimum linear locality of linear codes
The minimum linear locality of linear codes Open
Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory …
View article: Some punctured codes of several families of binary linear codes
Some punctured codes of several families of binary linear codes Open
Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by $\mathcal{C}(f)=\left\{ {\rm Tr}(af(x)+bx)_{x \in \mathbb{F}_{q^m}^*}: a,b \in \mathbb{F…
View article: An Infinite Family of Linear Codes Supporting 4-Designs
An Infinite Family of Linear Codes Supporting 4-Designs Open
The question as to whether there exists an infinite family of near MDS codes holding an infinite family of t-designs for t ≥ 2 was answered in the recent paper [Infinite families of near MDS codes holding t-designs, IEEE Trans. Inf. Theory…
View article: The Projective General Linear Group $\mathrm{PGL}_2(\mathrm{GF}(2^m))$ and Linear Codes of Length $2^m+1$
The Projective General Linear Group $\mathrm{PGL}_2(\mathrm{GF}(2^m))$ and Linear Codes of Length $2^m+1$ Open
The projective general linear group $\mathrm{PGL}_2(\mathrm{GF}(2^m))$ acts as a $3$-transitive permutation group on the set of points of the projective line. The first objective of this paper is to prove that all linear codes over $\mathr…
View article: The construction and weight distributions of all projective binary linear codes
The construction and weight distributions of all projective binary linear codes Open
Boolean functions can be used to construct binary linear codes in many ways, and vice versa. The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the Wa…
View article: The linear codes of t-designs held in the Reed-Muller and Simplex codes
The linear codes of t-designs held in the Reed-Muller and Simplex codes Open
A fascinating topic of combinatorics is $t$-designs, which have a very long history. The incidence matrix of a $t$-design generates a linear code over GF$(q)$ for any prime power $q$, which is called the linear code of the $t$-design over …
View article: The Subfield Codes of $[q+1, 2, q]$ MDS Codes
The Subfield Codes of $[q+1, 2, q]$ MDS Codes Open
Recently, subfield codes of geometric codes over large finite fields $\gf(q)$ with dimension $3$ and $4$ were studied and distance-optimal subfield codes over $\gf(p)$ were obtained, where $q=p^m$. The key idea for obtaining very good subf…
View article: Shortened Linear Codes over Finite Fields
Shortened Linear Codes over Finite Fields Open
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear code…
View article: Shortened linear codes from APN and PN functions
Shortened linear codes from APN and PN functions Open
Linear codes generated by component functions of perfect nonlinear (PN) and almost perfect nonlinear (APN) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper…