Date：2^nd-5^th, May

Venue：Room 617, School of Mathematical Science

Speaker：Chaoping Xing   Professor  Shanghai Jiao Tong University

Title：A survey on list decoding

Abstract：In this talk, I will first introduce background on list decoding and relation with Shannon's capacity theory. We then discuss list decodbility of random codes, Johnson bound on list decoding. Finally, we investigate list decoding of codes over large alphabets as well as small alphabets.

Speaker：Yonglin Cao   Professor  Shandong University of Technology

Title：Expressing all distinct self-dual cyclic codes of length $p^k$ over Galois ring ${\rm GR}(p^2,m)$

Abstract：Let $p$ be any odd prime number and let $m, k$ be arbitrary positive integers.The construction for self-dual cyclic codes of length $p^k$ over the Galois ring ${\rm GR}(p^2,m)$ is the key to construct self-dual cyclic codes of arbitrary length $p^kn$ over the integer residue class ring $\mathbb{Z}_{p^2}$ for any positive integer $n$ satisfying ${\rm gcd}(p,n)=1$.So far, existing literature has only determined the number of these self-dual cyclic codes [Des. Codes Cryptogr. {\bf  63}, 105--112 (2012)]. In this talk, we give an efficient construction for all distinct self-dual cyclic codes of length $p^k$ over ${\rm GR}(p^2,m)$ by using column vectors of Kronecker products of matrices with specific types. On this basis, we further obtain an explicit expression for all these self-dual cyclic codes by using combination numbers.

Speaker：Hongwei Liu    Professor  Central China Normal University

Title：A Survey on Matrix Product Codes over Finite Commutative

Abstract：Constructing codes from smaller ones and discussing their properties via those of smaller ones is an important and hot topic. Blackmore and Norton (2001) introduced the notion of matrix product codes

over finite fields, which is a generalization of many well-known constructions of codes, such as the $(u|u+v)$-construction, etc. An analogous study on matrix product codes over finite chain rings was given by van Asch in 2008. We investigated a very general case, i.e., matrix product codes over finite commutative Frobenius rings, and proposed a larger class of matrices, i.e., strongly full-row-rank matrices. The algebraic structures of the codes were exhibited, and lower bounds of minimum Hamming distances were generalized. The homogeneous distance was also studied for the case of finite principal ideal rings (PIRs). In this survey, we summarize these recent works on matrix product codes over finite commutative Frobenius rings.

Speaker：Xiwang Cao    Professor  Nanjing University of Aeronautics and Astronautics

Title：Three new constructions of asymptotically optimal PQCSS with small alphabet sizes

Abstract：Quasi-complementary sequence sets (QCSSs) play an important role in multi-carrier code-division multiple-access (MC-CDMA) systems. They can support more users than perfect complementary sequence sets in MC-CDMA systems. It is desirable to design QCSSs with good parameters that are a trade-off of large set size, small periodic maximum magnitude correlation and small alphabet size. The main results are to construct new infinite families of QCSSs that all have small alphabet size and asymptotically optimal periodic maximum magnitude correlation. In this paper, we propose three new constructions of QCSSs using additive characters over finite fields. Notably, these QCSSs have new parameters and small alphabet sizes. Using the properties of characters and character sums, we determine their maximum periodic correlation magnitudes and prove that these QCSSs are asymptotically optimal with respect to the lower bound.

Students and teachers are welcome.