Related papers: Difference Methods for Double-Change Covering Desi…
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…
A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N>=2) non-overlapping…
We construct codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ with $u^2=0$. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint and avoid…
We present constructions and results about GDDs with two groups and block size 6. We study those GDDs in which each block has configuration (s,t), that is in which each block has exactly s points from one of the two groups and t points from…
The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an…
Multivariate multiplicity codes have been recently explored because of their importance for list decoding and local decoding. Given a multivariate multiplicity code, in this paper, we compute its dimension using Gr\"obner basis tools, its…
Given two $k$-dicolourings of a digraph $D$, we prove that it is PSPACE-complete to decide whether we can transform one into the other by recolouring one vertex at each step while maintaining a dicolouring at any step even for $k=2$ and for…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC…
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an…
Complex orthogonal design (COD) with parameter $[p, n, k]$ is a combinatorial design used in space-time block codes (STBCs). For STBC, $n$ is the number of antennas, $k/p$ is the rate, and $p$ is the decoding delay. A class of rate $1/2$…
Code loops are certain Moufang $2$-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of…
Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the search as a continuous optimization. But…
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…
A new construction for moderate density parity-check (MDPC) codes using finite geometry is proposed. We design a parity-check matrix for this family of binary codes as the concatenation of two matrices: the incidence matrix between points…
Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…
This paper focuses on controlling the absorbing set spectrum for a class of regular LDPC codes known as separable, circulant-based (SCB) codes. For a specified circulant matrix, SCB codes all share a common mother matrix, examples of which…
The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points such that every two blocks intersect each other in $\lambda$ points (and $\lambda < v$ is a fixed number) and…
This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an $(n-1,w)$-difference triangle set are used as supports of the columns of rate…