Together with Marco Timpanella (University of Perugia) and Giovanni Zini (University of Modena and Reggio Emilia), the research group organize monthly seminars.
26 November 2026 [4.00 pm - Italian time] - Angelica Piccirillo (Technical University of Munich, Germany)
Title: Decoding Desarguesian spread codes beyond half minimum distance
Abstract: Spread codes are a well-known family of constant-dimension subspace-metric codes. For constant dimension k and ambient space dimension n being a multiple of k, these codes have minimum distance 2k and a rich geometric structure. In this talk I will illustrate the decoding capabilities of the nearest neighbor decoder for Desarguesian spread codes by establishing a connection with the geometric notion of subspaces that are evasive with respect to a Desarguesian spread. This connection shows that unique decoding remains achievable beyond half the minimum subspace distance. At the same time, it also reveals an intrinsic limitation on the dimension of random insertions that can be decoded reliably from the received subspace alone. Motivated by this, we develop a new decoding algorithm to uniquely decode Desarguesian spread codes in the presence of both insertions and deletions, which increase and decrease, respectively, the dimension of the transmitted codeword. In particular, our approach can handle the case where the received subspace has dimension larger than the codeword, i.e., when insertions outnumber deletions, with a success probability quickly converging to one as the field size increases. We also propose two refinements to this algorithm that, empirically, can handle nearly as many insertions as the nearest neighbor decoder. This is a joint work with Ermes Franch and Chunlei Li.