相关论文: The Cyclic Cutwidth of $Q_n$

We study embeddings of the $n$-dimensional hypercube into the circuit with $2^n$ vertices. We prove that the circular wirelength attains minimum by gray coding, which is called the CT conjecture by Chavez and Trapp (Discrete Applied…

It is known that the $n$-dimensional hypercube $Q_n,$ for $n$ even, has a decomposition into $k$-cycles for $k=n, 2n,$ $2^l$ with $2 \leq l \leq n.$ In this paper, we prove that $Q_n$ has a decomposition into $2^mn$-cycles for $n \geq 2^m.$…

Generalizations of QCD in which the number of colors N is taken to infinity are characterized by profound mathematical properties, with far-reaching implications for fundamental problems and for phenomenological issues alike. In this…

The $n$-dimensional hypercube network $Q_n$ is one of the most popular interconnection networks since it has simple structure and is easy to implement. The $n$-dimensional locally twisted cube, denoted by $LTQ_n$, an important variation of…

Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…

We consider edge decompositions of the $n$-dimensional hypercube $Q_n$ into isomorphic copies of a given graph $H$. While a number of results are known about decomposing $Q_n$ into graphs from various classes, the simplest cases of paths…

The cut polytope ${\rm CUT}(n)$ is the convex hull of the cut vectors in a complete graph with vertex set $\{1,\ldots,n\}$. It is well known in the area of combinatorial optimization and recently has also been studied in a direct relation…

Let Q_n be the graph of n times n times n cube with all non-decreasing diagonals (including the facial ones) in its constituent unit cubes. Suppose that a subset S of V(Q_n) separates the left side of the cube from the right side. We show…

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.…

The square $C^{*2}$ of a linear error correcting code $C$ is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in $C$. Squares of codes have gained attention for several applications…

The varietal hypercube $VQ_n$ is a variant of the hypercube $Q_n$ and has better properties than $Q_n$ with the same number of edges and vertices. This paper shows that every edge of $VQ_n$ is contained in cycles of every length from 4 to…

Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…

Given pairwise distinct vertices $\{\alpha_i , \beta_i\}^k_{i=1}$ of the $n$-dimensional hypercube $Q_n$ such that the distance of $\alpha_i$ and $\beta_i$ is odd, are there paths $P_i$ between $\alpha_i$ and $\beta_i$ such that $\{V…

In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…

In this paper, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic…

A cycle cover of a graph is a collection of cycles such that each edge of the graph is contained in at least one of the cycles. The length of a cycle cover is the sum of all cycle lengths in the cover. We prove that every bridgeless cubic…

We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an…

In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…

Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…

{A cyclic subspace code is a union of the orbits of subspaces contained in it. In a recent paper, Gluesing-Luerssen et al. (Des. Codes Cryptogr. 89, 447-470, 2021) showed that the study of the distance distribution of a single orbit cyclic…