Optimal Binary Subspace Codes of Length 6, Constant Dimension 3 and Minimum Distance 4

It is shown that the maximum size of a binary subspace code of packet length $v=6$, minimum subspace distance $d=4$, and constant dimension $k=3$ is $M=77$; in Finite Geometry terms, the maximum number of planes in $\operatorname{PG}(5,2)$ mutually intersecting in at most a point is $77$. Optimal binary $(v,M,d;k)=(6,77,4;3)$ subspace codes are classified into $5$ isomorphism types, and a computer-free construction of one isomorphism type is provided. The construction uses both geometry and finite fields theory and generalizes to any $q$, yielding a new family of $q$-ary $(6,q^6+2q^2+2q+1,4;3)$ subspace codes

Flag codes from planar spreads in network coding

In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space Fnq, being qa prime power and Fqthe finite field of qelements. In particular, we focus on flag codes having maximum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For n =2k, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm.The first and third authors are partially supported by Projecte AICO/2017/128 of Generalitat Valenciana. The second author is supported by Generalitat Valenciana and Fondo Social Europeo. Grants: ACIF/2018/196 and BEFPI/2019/070. The third author is also supported by the grant BEST/2019/192 of Generalitat Valenciana

Cooperative strategies design based on the diversity and multiplexing tradeoff

This thesis focuses on designing wireless cooperative communication strategies that are either optimal or near-optimal in terms of the tradeoff between diversity and multiplexing gains. Starting from classical cooperative broadcast, multiple-access and relay channels with unit degree of freedom, to more general cooperative interference channels with higher degrees of freedom, properties of different network topologies are studied and their unique characteristics together with several advanced interference management techniques are exploited to design cooperative transmission strategies in order to enhance data rate, reliability or both at the same time. Moreover, various algorithms are proposed to solve practical implementation issues and performance is analyzed through both theoretical verifications and simulations

Conflict detection in software-defined networks

The SDN architecture facilitates the flexible deployment of network functions. While promoting innovation, this architecture induces yet a higher chance of conflicts compared to conventional networks. The detection of conflicts in SDN is the focus of this work. Restrictions of the formal analytical approach drive our choice of an experimental approach, in which we determine a parameter space and a methodology to perform experiments. We have created a dataset covering a number of situations occurring in SDN. The investigation of the dataset yields a conflict taxonomy composed of various classes organized in three broad types: local, distributed and hidden conflicts. Interestingly, hidden conflicts caused by side-effects of control applications‘ behaviour are completely new. We introduce the new concept of multi-property set, and the ·r (“dot r”) operator for the effective comparison of SDN rules. With these capable means, we present algorithms to detect conflicts and develop a conflict detection prototype. The evaluation of the prototype justifies the correctness and the realizability of our proposed concepts and methodologies for classifying as well as for detecting conflicts. Altogether, our work establishes a foundation for further conflict handling efforts in SDN, e.g., conflict resolution and avoidance. In addition, we point out challenges to be explored. Cuong Tran won the DAAD scholarship for his doctoral research at the Munich Network Management Team, Ludwig-Maximilians-Universität München, and achieved the degree in 2022. He loves to do research on policy conflicts in networked systems, IP multicast and alternatives, network security, and virtualized systems. Besides, teaching and sharing are also among his interests