Algebra Seminar: On linear codes from incidence geometries

Algebra Seminar: On linear codes from incidence geometries

Speaker: Michel Lavrauw, Sabancı University

Title: On linear codes from incidence geometries  

Date/Time: October 9, 2019  /  13.40-14.30

Place: FENS G035

Abstract: The characterisation of minimum weight codewords in linear codes is a classical problem within coding theory. Of special interest are the codes generated by the incidence matrix of points and blocks of certain incidence structures. The codes generated by the incidence matrix of points and subspaces of affine and projective spaces are well understood since the 1970's through their relation with the Reed-Muller codes. For partial geometries, the duals of these codes have attracted attention because of their properties when seen as an LDPC code, and the minimum weight has been determined in several cases [1, 2, 3]. However, when the partial geometry is not fully embedded in affine or projective space, far less is known. In this talk we will report on recent work with Geertui Van de Voorde in which we solve this problem for translation generalised quadrangles, thus extending the known results for classical generalised quadrangles from [4].

References

[1] S.J. Johnson and S.R. Weller. Codes for iterative decoding from partial geometries. IEEE Trans. Comm. 52 (2004), 236{243

[2] J.L. Kim, K.E. Mellinger, and L. Storme. Small weight codewords in LDPC codes de ned by (dual) classical generalised quadrangles. Des. Codes Cryptogr. 42 (1) (2007), 73{92.

[3] V. Pepe, L. Storme, and G. Van de Voorde. Small weight codewords in the LDPC codes arising from linear representations of geometries. J. Combin. Des. 17 (1) (2009), 1{24.

[4] B. Bagchi and N.S.N. Sastry. Codes associated with generalized polygons. Geom. Ded- icata 27 (1) (1988), 1{8.

BIO: Michel Lavrauw studied Mathematics at Ghent University (Belgium), and obtained a Ph.D. degree in Mathematics from Eindhoven University of Technology (The Netherlands) in 2001 under the supervision of Aart Blokhuis and Andries Brouwer. He worked as a postdoc at the University of Naples (Marie Curie Fellowship), at Universitat Politècnica de Catalunya in Barcelona (EU-project COMBSTRU), at Eindhoven University of Technology (Veni grant (NWO)), at Ghent University (FWO fellowship), and at Vrije Universiteit Brussel (VUB). In 2012, he obtained the Abilitazione Scientifica Nazionale for full professor (settore 01/A1, Algebra/Geomety) from the Italian Ministero dell'Istruzione dell'Università e della Ricerca, and was a faculty member at the University of Padua (Italy) from 2011-2017. In 2017 he joined the Math group of the Faculty of Engineering and Natural Sciences at Sabancı University.

Contact: Michel Lavrauw