8 papers · 1 filter
A New Invariant for Prime Alternating Knots From Error-Correcting Codes
Altan B. Kilic, Ruud Pellikaan, Alberto Ravagnan
This paper shows that the Alexander-Briggs code of a knot gives rise to a new invariant that distinguishes prime alternating knots. The restriction to prime alternating knots preci…
Capacity of Non-Separable Networks with Restricted Adversaries
Christopher Hojny, Altan B. Kılıç, Sascha Kurz +1
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to opera…
The Length of Functional Batch and PIR Codes
Altan B. Kilic, Alberto Ravagnani, Flavio Salizzoni
We consider the problem of computing the minimum length of functional batch and PIR codes of fixed dimension and for a fixed list size, over an arbitrary finite field. We recover,…
On the Parameters of Codes for Data Access
Altan B. Kilic, Alberto Ravagnani, Emina Soljanin
This paper studies two crucial problems in the context of coded distributed storage systems directly related to their performance: 1) for a fixed alphabet size, determine the minim…
Rank-Metric Codes and Their Parameters
Anina Gruica, Altan B. Kilic, Alberto Ravagnani
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum r…
Knot Theory and Error-Correcting Codes
Altan B. Kilic, Anne Nijsten, Ruud Pellikaan +1
This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting c…
Network Coding: An Optimization Approach
Christopher Hojny, Altan B. Kilic, Alberto Ravagnani
We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programm…
Network Decoding
Allison Beemer, Altan Berdan Kilic, Alberto Ravagnani
We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model t…