Michael Braun
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Michael Braun has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
- Alfred Wassermann
Department of Mathematics, University of Bayreuth, Bayreuth, Germany
4 shared publications Alfred Wassermann
University of Bayreuth
3 shared publications- Michael Kiermaier
Department of Mathematics, University of Bayreuth, Bayreuth, Germany
3 shared publications - Alexander Vardy
Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA, USA
2 shared publications - Andrea Švob
Faculty of Mathematics, University of Rijeka, Rijeka, CROATIA
2 shared publications Axel Kohnert
2 shared publications
Latest Publications
- Open Access
- 19 March 2025
- Published by Combinatorial Press in Journal of Combinatorial Mathematics and Combinatorial Computing
- Vol. 124, 745-751
On the automorphism group of putative \((n,r)\)-arcs in \(\operatorname{PG}(2,11)\) and \(\operatorname{PG}(2,13)\)An \( (n,r) \)-arc in \( \operatorname{PG}(2,q) \) is a set \( \mathcal{B} \) of points in \( \operatorname{PG}(2,q) \) such that each line in \( \operatorname{PG}(2,q) \) contains at most \( r \) elements of \( \mathcal{B} \) and such that there is at least one line containing exactly \( r \) elements of \( \mathcal{B} \). The value \( m_r(2,q) \) denotes the maximal number \( n \) of points in the projective geometry \( \operatorname{PG}(2,q) \) for which an \( (n,r) \)-arc exists. We show by systematically excluding possible automorphisms that putative \( (44,5) \)-arcs, \( (90,9) \)-arcs in \( \operatorname{PG}(2,11) \), and \( (39,4) \)-arcs in \( \operatorname{PG}(2,13) \)---in case of their existence---are rigid, i.e. they all would only admit the trivial automorphism group of order \( 1 \). In addition, putative \( (50,5) \)-arcs, \( (65,6) \)-arcs, \( (119,10) \)-arcs, \( (133,11) \)-arcs, and \( (146,12) \)-arcs in \( \operatorname{PG}(2,13) \) would be rigid or would admit a unique automorphism group (up to conjugation) of order \( 2 \).- 19 March 2025
- Published by Combinatorial Press in Journal of Combinatorial Mathematics and Combinatorial Computing
- Vol. 124, 745-751
Open AccessOn the automorphism group of putative \((n,r)\)-arcs in \(\operatorname{PG}(2,11)\) and \(\operatorname{PG}(2,13)\)An \( (n,r) \)-arc in \( \operatorname{PG}(2,q) \) is a set \( \mathcal{B} \) of points in \( \operatorname{PG}(2,q) \) such that each line in \( \operatorname{PG}(2,q) \) contains at most \( r \) elements of \( \mathcal{B} \) and such that there is at least one line containing exactly \( r \) elements of \( \mathcal{B} \). The value \( m_r(2,q) \) denotes the maximal number \( n \) of points in the projective geometry \( \operatorname{PG}(2,q) \) for which an \( (n,r) \)-arc exists. We show by systematically excluding possible automorphisms that putative \( (44,5) \)-arcs, \( (90,9) \)-arcs in \( \operatorname{PG}(2,11) \), and \( (39,4) \)-arcs in \( \operatorname{PG}(2,13) \)---in case of their existence---are rigid, i.e. they all would only admit the trivial automorphism group of order \( 1 \). In addition, putative \( (50,5) \)-arcs, \( (65,6) \)-arcs, \( (119,10) \)-arcs, \( (133,11) \)-arcs, and \( (146,12) \)-arcs in \( \operatorname{PG}(2,13) \) would be rigid or would admit a unique automorphism group (up to conjugation) of order \( 2 \). - 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Advances in Mathematics of Communications
Full flag codes are the $ q $-analog of permutation codes with the Manhattan metric
In this article we prove that full flag codes are the $ q $-analog of permutation codes equipped with the Manhattan metric by the following approach: First, we consider the set $ \text{Ch}(P(n),t) $ of finite chains of length $ t $ of nested subsets of an $ n $ element set and prove that this set forms a metric space. We show the connection of $ \text{Ch}(P(n),t) $ to the metric space $ {\mathbb Z}_{t+1}^n $ equipped with the Manhattan distance. In particular, sets of full chains of subsets for $ t = n-1 $ form permutation codes with respect to the Manhattan distance. As a consequence, by replacing subsets by subspaces and cardinalities by dimensions we obtain that flag codes for network coding are obviously the $ q $-analog of sets of full chains of subsets and hence the $ q $-analog of permutation codes equipped with Manhattan metric as well.- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Advances in Mathematics of Communications
Full flag codes are the $ q $-analog of permutation codes with the Manhattan metric
In this article we prove that full flag codes are the $ q $-analog of permutation codes equipped with the Manhattan metric by the following approach: First, we consider the set $ \text{Ch}(P(n),t) $ of finite chains of length $ t $ of nested subsets of an $ n $ element set and prove that this set forms a metric space. We show the connection of $ \text{Ch}(P(n),t) $ to the metric space $ {\mathbb Z}_{t+1}^n $ equipped with the Manhattan distance. In particular, sets of full chains of subsets for $ t = n-1 $ form permutation codes with respect to the Manhattan distance. As a consequence, by replacing subsets by subspaces and cardinalities by dimensions we obtain that flag codes for network coding are obviously the $ q $-analog of sets of full chains of subsets and hence the $ q $-analog of permutation codes equipped with Manhattan metric as well.- Open Access
- 7 November 2023
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 693, 362-373
q-analogs of strongly regular graphs
- 7 November 2023
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 693, 362-373
Open Accessq-analogs of strongly regular graphs
- Open Access
- 23 December 2022
- Published by Springer Nature in Annals of Telecommunications
- Vol. 78 (1-2) , 33-51
Efficient practical Byzantine consensus using random linear network coding
Using random linear network coding (RLNC) in asynchronous networks with one-to-many information flow has already been proven to be a valid approach to maximize the channel capacities. Message-based consensus protocols such as practical Byzantine fault tolerance (pBFT) adhere partially to said scenario. Protocol phases with many-to-many communication, however, still suffer from quadratic growth in the number of required transmissions to reach consensus. We show that an enhancement in the data transmission behavior in the quadratic phases is possible through combining RLNC with pBFT as one hybrid protocol. We present several experiments conducted on random network topologies. We conclude that using RLNC-based data transmission offers a significantly better performance under specific circumstances, which depend on the number of participating network nodes and the chosen coding parameters. Applying the same approach to other combinations of message-based consensus and network coding protocols promises not only a gain in performance, but may also improve robustness and security and open up new application scenarios for RLNC, e.g., running it on the application layer.
- 23 December 2022
- Published by Springer Nature in Annals of Telecommunications
- Vol. 78 (1-2) , 33-51
Open AccessEfficient practical Byzantine consensus using random linear network coding
Using random linear network coding (RLNC) in asynchronous networks with one-to-many information flow has already been proven to be a valid approach to maximize the channel capacities. Message-based consensus protocols such as practical Byzantine fault tolerance (pBFT) adhere partially to said scenario. Protocol phases with many-to-many communication, however, still suffer from quadratic growth in the number of required transmissions to reach consensus. We show that an enhancement in the data transmission behavior in the quadratic phases is possible through combining RLNC with pBFT as one hybrid protocol. We present several experiments conducted on random network topologies. We conclude that using RLNC-based data transmission offers a significantly better performance under specific circumstances, which depend on the number of participating network nodes and the chosen coding parameters. Applying the same approach to other combinations of message-based consensus and network coding protocols promises not only a gain in performance, but may also improve robustness and security and open up new application scenarios for RLNC, e.g., running it on the application layer.
- Open Access
$q$-Analogs of strongly regular graphs
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
Open Access$q$-Analogs of strongly regular graphs
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
- 30 April 2022
- Published by International Electronic Journal of Geometry, Person (Kazim ILARSLAN) in International Electronic Journal of Geometry
- Vol. 15 (1) , 69-74
On the Computation of Conjugation Classes of Elements of PGL(3, q)
In this article an explicit list of representatives of all conjugacy classes of the projective linear group $\pgl(3,q)$ is computed with complexity $O(q^2)$.- 30 April 2022
- Published by International Electronic Journal of Geometry, Person (Kazim ILARSLAN) in International Electronic Journal of Geometry
- Vol. 15 (1) , 69-74
On the Computation of Conjugation Classes of Elements of PGL(3, q)
In this article an explicit list of representatives of all conjugacy classes of the projective linear group $\pgl(3,q)$ is computed with complexity $O(q^2)$.- Open Access
- 21 August 2019
- Published by Wiley in Journal of Combinatorial Designs
- Vol. 27 (11) , 682-687
New lower bounds on the size of (n,r)‐arcs in PG(2,q)
An <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arc in <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> is a set of <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> points such that each line contains at most <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> of the selected points. It is well known that <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arcs in <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> correspond to projective linear codes. Let <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> denote the maximal number <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> of points for which an <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arc in <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> exists. In this paper we obtain improved lower bounds on <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> by explicitly constructing <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arcs. Some of the constructed <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.- 21 August 2019
- Published by Wiley in Journal of Combinatorial Designs
- Vol. 27 (11) , 682-687
Open AccessNew lower bounds on the size of (n,r)‐arcs in PG(2,q)
An <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arc in <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> is a set of <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> points such that each line contains at most <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> of the selected points. It is well known that <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arcs in <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> correspond to projective linear codes. Let <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> denote the maximal number <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> of points for which an <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arc in <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> exists. In this paper we obtain improved lower bounds on <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> by explicitly constructing <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arcs. Some of the constructed <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> ‐arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming. - Open Access
New lower bounds on the size of (n,r)-arcs in PG(2,q)
An (n,r)-arc in PG(2,q) is a set of n points such that each line contains at most r of the selected points. It is well-known that (n,r)-arcs in PG(2,q) correspond to projective linear codes. Let m_r(2,q) denote the maximal number n of points for which an (n,r)-arc in PG(2,q) exists. In this paper we obtain improved lower bounds on m_r(2,q) by explicitly constructing (n,r)-arcs. Some of the constructed (n,r)-arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.
Open AccessNew lower bounds on the size of (n,r)-arcs in PG(2,q)
An (n,r)-arc in PG(2,q) is a set of n points such that each line contains at most r of the selected points. It is well-known that (n,r)-arcs in PG(2,q) correspond to projective linear codes. Let m_r(2,q) denote the maximal number n of points for which an (n,r)-arc in PG(2,q) exists. In this paper we obtain improved lower bounds on m_r(2,q) by explicitly constructing (n,r)-arcs. Some of the constructed (n,r)-arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.
- Open Access
- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Advances in Mathematics of Communications
- Vol. 13 (1) , 165-170
New 2-designs over finite fields from derived and residual designs
Based on the existence of designs for the derived and residual parameters of admissible parameter sets of designs over finite fields we obtain a new infinite series of designs over finite fields for arbitrary prime powers $q$ with parameters $2\text{-}(8,4,\frac{(q^6-1)(q^3-1)}{(q^2-1)(q-1)};q)$ as well as designs with parameters $2\text{-}(10,4,85λ;2)$, $2\text{-}(10,5,765λ;2)$, $2\text{-}(11,5,6205λ;2)$, $2\text{-}(11,5,502605λ;2)$, and $2\text{-}(12,6,423181λ;2)$ for $λ = 7,12,19,21,22,24,31,36,42,43,48,49,55,60,63$.- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Advances in Mathematics of Communications
- Vol. 13 (1) , 165-170
Open AccessNew 2-designs over finite fields from derived and residual designs
Based on the existence of designs for the derived and residual parameters of admissible parameter sets of designs over finite fields we obtain a new infinite series of designs over finite fields for arbitrary prime powers $q$ with parameters $2\text{-}(8,4,\frac{(q^6-1)(q^3-1)}{(q^2-1)(q-1)};q)$ as well as designs with parameters $2\text{-}(10,4,85λ;2)$, $2\text{-}(10,5,765λ;2)$, $2\text{-}(11,5,6205λ;2)$, $2\text{-}(11,5,502605λ;2)$, and $2\text{-}(12,6,423181λ;2)$ for $λ = 7,12,19,21,22,24,31,36,42,43,48,49,55,60,63$. - Open Access
- 1 March 2018
- Published by Elsevier in Electronic Notes in Discrete Mathematics
- Vol. 65, 23-29
Disjoint q -Steiner systems in dimension 13
- 1 March 2018
- Published by Elsevier in Electronic Notes in Discrete Mathematics
- Vol. 65, 23-29
Open AccessDisjoint q -Steiner systems in dimension 13