The workshop was organized by the Vietnam Institute for Advanced Study in Mathematics (VIASM) at the 7th floor, Ta Quang Buu Library in HUST’s Campus, Ha Noi, from 25 to 27/12/2019. There are about 25 participants including three from abroad and many Vietnamese researchers from many provinces such as Ho Chi Minh city, Hue, Da Nang, Vinh, Ha Tinh, Thanh Hoa, Ba Ria – Vung Tau, Ha Noi, Vinh Long, …
The workshop had a lecture series about coding theory, a lecture series about cryptography and a section on structures of rings and theory of modules. The first lecture series include 8 topics: 1) Introduction to algebraic coding theory: the choice of alphabets, 2) Basic concepts in codes and rings, 3) Cyclic codes over finite commutative rings: the simple-root case, 4) Galois extension rings of F2+uF2 and their use as code-alphabets, 5) Repeated-root contacyclic codes of prime power length over finite chain rings, 6) Repeated-root constacyclic codes of length p^s over F+uF, 7) Repeated-root constacyclic codes of length 2p^s and 4p^s over F+uF, 8) Skew constacyclic codes over finite fields and finite chain rings. In this lecture series, Prof. Hai Q. Dinh (Kent State University, USA) discussed the historical background of Algebraic Coding Theory, and how new researchers can start doing research in Coding Theory by studying the algebraic structure of the so-called constacyclic codes. Foundational and theoretical aspects of the role of finite rings as alphabets in coding theory were discussed, with a concentration on the class of constacyclic codes over finite commutative chain rings. Both the simple-root and repeated-root cases were studied. Several generalizations in which the notion of constacyclicity has been extended were also provided. Among others, some applications and open directions for future research were presented.
The second lecture series includes two topics, which were presented by Dr. Abhay Kumar Singh (Indian Institute of Technology Dhanbad, India). The first topic is about DNA Cyclic Codes over Finite Rings. He discussed the DNA code construction of general length over the ring Z4+vZ4, v^2=v and GC-weight of DNA codes. Later, he presented the structure of DNA cyclic codes of odd lengths over some rings. The second topic is an overview on Code-based cryptography.
About the section on rings and theory of modules, Truong Cong Quynh, Da Nang University gave an invited 50-minute-talk about modules close to the automorphism-invariant and coinvariant. He studied the class of automorphism-invariant modules and the class of automorphism-coinvariant modules, then generalized them to X-automorphism-invariant modules, X-idempotent-invariant modules.... This section also had six 15-minute talks: A note on ring whose maximal right ideals are finitely generated (Le Van Thuyet, Hue University), Characterizations of rings using quasi-injective modules (Phan Dan, Hong Bang International University), A note on Harada rings (Banh Duc Dung, Ho Chi Minh City University of Technology and Education), Some characterizations of A-C3 modules (Tran Hoai Ngoc Nhan, Vinh Long University of Technology and Education), On essentially injective modules (Nguyen Thi Thu Ha, Industrial University of Ho Chi Minh City), A note on automorphism-invariant modules (Dao Thi Trang, Ho Chi Minh City University of Food Industry).
The Workshop achieved good results satisfying two aims: the first is to present the new results in the fields of ring, module and coding theory. Other aim is giving two lecture series on coding theory and cryptography and these lectures cover from very basic knowledge to some open research problems.