Related papers: In search of maximum non-overlapping codes
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…
The groupcast index coding problem is the most general version of the classical index coding problem, where any receiver can demand messages that are also demanded by other receivers. Any groupcast index coding problem is described by its…
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
Which nonlocal correlations can be obtained, when a party has access to more than one subsystem? While traditionally nonlocality deals with spacelike separated parties, this question becomes important with quantum technologies that connect…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
In this paper we study equidistant subspace codes, i.e. subspace codes with the property that each two distinct codewords have the same distance. We provide an almost complete classification of such codes under the assumption that the…
In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
The genetic code has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimisation problem as a Quadratic…
The maximum possible number of non-overlapping unit spheres that can touch a unit sphere in $n$ dimensions is called kissing number. The problem for finding kissing numbers is closely connected to the more general problems of finding bounds…
This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar…
Network coding is known to improve the throughput and the resilience to losses in most network scenarios. In a practical network scenario, however, the accurate modeling of the traffic is often too complex and/or infeasible. The goal is…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…