相关论文: On Optimal Index Codes for Interlinked Cycle Struc…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length $n$ over the ring $\mathbb{Z}_4$ have been focused on.…
In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
Index coding is concerned with efficient broadcast of a set of messages to receivers in the presence of receiver side information. In this paper, we study the secure index coding problem with security constraints on the receivers…
Finding the common structural features of two molecules is a fundamental task in cheminformatics. Most drugs are small molecules, which can naturally be interpreted as graphs. Hence, the task is formalized as maximum common subgraph…
We focus on the following instance of an index coding problem, where a set of receivers are required to decode multiple messages, whilst each knows one of the messages a priori. In particular, here we consider a generalized setting where…
In this work codes with availability are constructed based on the cyclic \emph{locally repairable code} (LRC) construction by Tamo et al. and their extension to $(r,\rho)$-locality by Chen et al. The minimum distance of these codes is…
In order to study real-world systems, many applied works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned…
We study zero-error unicast index-coding instances, where each receiver must perfectly decode its requested message set, and the message sets requested by any two receivers do not overlap. We show that for all these instances with up to…
The index coding problem is studied from an interference alignment perspective, providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between multiple unicast…
It is well known that the problem of determining the weight distributions of families of cyclic codes is, in general, notoriously difficult. An even harder problem is to find characterizations of families of cyclic codes in terms of their…
Motivated by applications in distributed storage and distributed computation, we introduce embedded index coding (EIC). EIC is a type of distributed index coding in which nodes in a distributed system act as both senders and receivers of…
We consider embeddings of maximal outerplanar graphs whose vertices all lie on a cycle $\mathcal{C}$ bounding a face. Each edge of the graph that is not in $\mathcal{C}$, a chord, is assigned a length equal to the length of the shortest…
The capacity of symmetric instance of the multiple unicast index coding problem with neighboring antidotes (side-information) with number of messages equal to the number of receivers was given by Maleki \textit{et al.} In this paper, we…
In this work we propose an encoding and decoding framework for staircase codes based on non-systematic polar codes as component codes. The staircase structure allows for efficient parallelized decoding, while the polar component codes allow…
In this paper we study the structure of $\theta$-cyclic codes over the ring $B_k$ including its connection to quasi-$\tilde{\theta}$-cyclic codes over finite field $\mathbb{F}_{p^r}$ and skew polynomial rings over $B_k.$ We also…
The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle.…
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and…