# Reports on Coding Theory

At the invitation of the school of mathematical science of Nanjing Normal University, Qin Yue, Professor of Nanjing University of Aeronautics and Astronautics, Xiwang Cao, Professor of Nanjing University of Aeronautics and Astronautics, Jun Zhang, Associate Professor of Capital Normal University, conducted an online academic exchange about the topic "Code Theory" by Tencent Conference(ID：638601672) on the morning of September 25, 2020. Professor Haiyan Zhou of the school of mathematical science presided over the seminar, and some teachers of the school of mathematical science, masters and doctoral students participated in the seminar.

Binary asymmetric error-correcting codes (AECC) play an important role in communication systems modeled by the binary asymmetric channel (Z-channel). Varshamov proposed a general construction of binary AECC via $V_h$-sequences and obtained many good binary AECC. Associate Professor Jun Zhang’s talk about “A construction of binary asymmetric error-correcting codes” gave a general construction of $V_h$-sequences in ray class groups of algebraic function fields, and induced new lower bounds for binary AECC which improve the former results.

In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are related to quantum state tomography, quantum cryptography and foundational studies. However, constructing SIC-POVMs is notoriously hard. Although some SIC-POVMs have been constructed numerically, there does not exist an infinite class of them. Professor Xiwang Cao introduced New constructions of approximately SIC-POVMs via difference sets: two constructions of approximately SIC-POVMs, where a small deviation from uniformity of the inner products is allowed.

Professor Qin Yue introduced Self-dual Codes, LCD Codes and Self-orthogonal Codes in Dihedral Group Algebras. In his talk, he used idempotent elements to construct self-dual codes in Dihedral group algebras and compute their parameters. Moreover, he counted the number of LCD codes and self-orthogonal codes in Dihedral group algebras.

At the end of the talks, the students and teachers here put forward their own questions about the contents of the talk, and three speakers gave the answers with more details. The seminar successful completed.