Periodic Reporting for period 1 - ACCENT (Algebraic Covering Codes Enabling Network Transmissions)
Okres sprawozdawczy: 2018-05-01 do 2020-04-30
The research focus of the project was on the mathematical properties of rank-metric error-correcting codes, with emphasis of their covering radii, (generalized) weight distributions, density properties and structural invariants. More details are included in the section “Progress beyond the state of the art”.
Rank-metric codes were proposed in 2008 as a solution to the problem of error amplification in network communications. Since then, they have been the subject of intense research among mathematicians, electrical engineers and computer scientists.
Besides the research objectives, the project also had the goal of strengthen the professional profile of the researcher and enhance his career perspectives via mentoring experience, training in proposal writing, and teaching experience.
Rank-metric codes were proposed in 2008 as a solution to the problem of error amplification in network communications. Since then, they have been the subject of intense research among mathematicians, electrical engineers and computer scientists.
Besides the research objectives, the project also had the goal of strengthen the professional profile of the researcher and enhance his career perspectives via mentoring experience, training in proposal writing, and teaching experience.
1) RESEARCH. Most of the project time was devoted to research. We tackled difficult open problems on the mathematics of error-correcting codes, with a particular focus on their structural properties (covering radius, density questions, tensor representation of codes, connections between codes and subspace designs, connections between codes and rook theory). Our findings resulted in various publications in refereed journals, conference proceedings, and research talks.
2) DISSEMINATION. Our results were disseminated via publications in journals, conference proceedings, and research talks at international conferences and seminars. The research outputs associated with the projects are as follows:
-- 7 papers published in international peer-reviewed journals or submitted for publication,
-- 3 papers in refereed conference proceedings,
-- 8 talks at international conferences/workshops,
-- 7 seminar talks.
A detailed list of talks and publications is provided in the technical report.
3) OUTREACH. The researcher held information sessions about scientific university studies in high schools.
4) MENTORING EXPERIENCE. The researcher co-supervised MSc and PhD students during the grant duration, acquiring mentoring experience.
5) TEACHING EXPERIENCE. The researcher acquired teaching experience as the lecturer of mathematics courses at BSc and MSc level.
6) PARTICIPATION TO CONFERENCES. The researcher participated to 10 international conferences/workshops during the grant period and to several research seminars in Europe. He was also regular participant of seminar series at his host institution.
2) DISSEMINATION. Our results were disseminated via publications in journals, conference proceedings, and research talks at international conferences and seminars. The research outputs associated with the projects are as follows:
-- 7 papers published in international peer-reviewed journals or submitted for publication,
-- 3 papers in refereed conference proceedings,
-- 8 talks at international conferences/workshops,
-- 7 seminar talks.
A detailed list of talks and publications is provided in the technical report.
3) OUTREACH. The researcher held information sessions about scientific university studies in high schools.
4) MENTORING EXPERIENCE. The researcher co-supervised MSc and PhD students during the grant duration, acquiring mentoring experience.
5) TEACHING EXPERIENCE. The researcher acquired teaching experience as the lecturer of mathematics courses at BSc and MSc level.
6) PARTICIPATION TO CONFERENCES. The researcher participated to 10 international conferences/workshops during the grant period and to several research seminars in Europe. He was also regular participant of seminar series at his host institution.
The main objectives of the proposal were overall achieved and several connected mathematical problems were studied and solved. Our work addressed various problems that can be summarized by topic as follows:
-- Density questions in the context of coding theory.
-- Rank-metric codes and combinatorial subspace designs.
-- Rank-metric codes and tensors.
-- Rank-metric codes and q-rook polynomials.
-- Enumerative combinatorics and geometric lattices.
-- Generalized zeta functions and binomial moments of error-correcting codes.
More details about each individual topic are provided in the technical report.
-- Density questions in the context of coding theory.
-- Rank-metric codes and combinatorial subspace designs.
-- Rank-metric codes and tensors.
-- Rank-metric codes and q-rook polynomials.
-- Enumerative combinatorics and geometric lattices.
-- Generalized zeta functions and binomial moments of error-correcting codes.
More details about each individual topic are provided in the technical report.