Related papers: Construction of Minimal Ternary Linear Codes with …
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. In this paper we prove an upper bound on the minimal…
In this paper we introduce and study line Hermitian Grassmann codes as those subcodes of the Grassmann codes associated to the $2$-Grassmannian of a Hermitian polar space defined over a finite field of square order. In particular, we…
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…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
A linear code of length $n$ over a finite chain ring $R$ with residue field $\F_q$ is a $R$-submodule of $R^n$. A $R$-linear code is a code over $\F_q$ (not necessarily linear) which is the generalized Gray map image of a linear code over…
Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${\cal C}$, identify…
In this paper we construct new Griesmer codes of dimension $k\geq 5$ by means of some geometric methods such as projective dual and geometric puncturing.
We study trace codes with defining set $L,$ a subgroup of the multiplicative group of an extension of degree $m$ of the alphabet ring $\mathbb{F}_3+u\mathbb{F}_3+u^{2}\mathbb{F}_{3},$ with $u^{3}=1.$ These codes are abelian, and their…
An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t\!>\!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage…
Currently, the existence of an extremal singly even self-dual code of length $24k+10$ is unknown for all nonnegative integers $k$. In this note, we study singly even self-dual $[24k+10,12k+5,4k+2]$ codes. We give some restrictions on the…
Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of…
Quantum Tanner codes are a class of quantum low-density parity-check codes that provably display a linear minimum distance and a constant encoding rate in the asymptotic limit. When built from left--right Cayley complexes, they can be…
Minimal codewords have applications in decoding linear codes and in cryptography. We study the number of minimal codewords in binary linear codes that arise by appending a unit matrix to the adjacency matrix of a graph.
Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
In this article we present a class of codes with few weights arising from special type of linear sets. We explicitly show the weights of such codes, their weight enumerator and possible choices for their generator matrices. In particular,…