At Aalborg University I was member of the research group Mathematics for Communication. In particular from 2011 to 2016 I collaborated with my PhD supervisors: Professor MSO Olav Geil and Associate Professor Diego Ruano. For this reason the bigger part of my papers has been published in collaboration with them.
A great collaboration has been mantained with Associate Professor Ryutaroh Matsumoto from Tokyo Institute of Technology. In his visit at Aalborg University two papers were written.
During the years of my PhD I was part of the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography (AGINCC). This center was composed by the partecipation of three universities: Aalborg University, DTU (Copenhagen) and East China Normal University (Shanghai). As member I visited China twice: the second time I stayed in Shanghai for three months.
In 2015 and 2016 I collaborated as associated researcher at the research project "How secret is a secret?" sponsored by The Danish Council for Independent Research - Natural Science.
More technical information about my research and project can be retrieved from my VBN page.
The topics of my research have been coding theory, cryptography and applied algebra. In collaboration with the algebra group of Aalborg University I developed experience in mathematical research. In particular in the last period I have focused on the security evaluation of a cryptographic system called "secret sharing". Application of this method can be seen in digital elections or wireless communication. We proved that its security can completely characterized by new linear code parameters called "Relative generalized Hamming weights".
On this topic I am coauthor in three papers: "Relative generalized Hamming weights of one-point algebraic geometric codes", "Relative generalized Hamming weights of q-ary Reed-Muller codes" and "On asymptotically good ramp secret sharing schemes". These papers analize secret sharing schemes respectively built on one-point algebraic geometric codes, Reed-Muller codes and asympotically good codes.
Previously I worked on a more pure coding theory topic. In particular I and professor Olav Geil analized the Geil-Anderson bound and we showrf its utility to bound the Relative General Hamming Weight of a linear code.
The following tables illustrate my papers.
COD: Coding Theory, CRY: Cryptography The coauthors are listed in alphabetical order.
|COD||O. Geil, S. Martin||Relative generalized Hamming weights of q-ary Reed-Muller codes||Accepted for publication||[ArXiv]|
|COD CRY||O. Geil, S. Martin, U. Martinez-Penas, R. Matsumoto, D. Ruano||On asymptotically good ramp secret sharing schemes||Accepted for publication||[ArXiv]|
|COD||O. Geil, S. Martin, U. Martinez-Penas, D. Ruano||Refined analysis of RGHWs of code pairs coming from Gracia-Stichtenoth's second tower||Journal of Algebra Combinatorics Discrete Structures and Applications [link]||[Doi]||[ArXiv]|
|COD CRY||O. Geil, S. Martin, R. Matsumoto, D. Ruano, Y. Luo||Relative generalized Hamming weights of one-point algebraic geometric codes||IEEE Transaction of Information Theory [link]||[Doi]||[ArXiv]|
|COD||O. Geil, S. Martin||An improvement of the Feng-Rao bound for primary codes||Designs, Codes and Cryptography [link]||[Doi]||[ArXiv]|
|COD||O. Geil, S. Martin||Further improvements on the Feng-Rao bound for dual codes||Finite Field and Applications [link]||[Doi]||[ArXiv]|
|COD||O. Geil, S. Martin, R. Matsumoto||A new method for constructing small-bias spaces from Hermitian codes||Arithmetic of Finite Fields: 4th International Workshop on the Arithmetic of Finite Fields, WAIFI 2012 [link]||[Doi]||[ArXiv]|