Linear codes have a wide range of applications in the data storage systems, communication systems and consumer electronics products. In this talk, we present four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including infinite families of (near) Griesmer codes. We characterize the optimality of these four families of linear codes with an explicit computable criterion using the Griesmer bound and obtain many distanceoptimal linear codes. In addition, by a more in-depth discussion on some special cases of these four families of linear codes, we obtain several classes of (distance-)optimal linear codes with few weights and completely determine their weight distributions. We also show that most of our linear codes are self-orthogonal or minimal which are useful in applications.
About the lecturer:
Li Nian is professor and doctoral supervisor of Hubei University. In 2013, he received his doctor's degree from Southwest Jiaotong University with Professor Tang Xiaohu as his supervisor; During the doctoral period, he was jointly trained at University of Bergen in Norway for two years, and his supervisor therein was Academician Tor Helleseth; In the following three years, he continued to work as a postdoctoral researcher on algebraic coding and cryptography at Hong Kong University of Science and Technology and University of Bergen, with cooperating advisors as professors Xiong Maosheng and Lilya Budaghyan. He mainly studies cryptography, coding and related mathematical theories. In recent years, he has made a series of achievements in the fields of cryptographic function, linear code, sequence design, etc. He has presided over 2 programs of the National Natural Science Foundation of China and 3 programs of provincial and ministerial funds including the Outstanding Talents in Hubei Province. His representative achievements have been published in important domestic and foreign academic journals includingIEEE Transactions on Information Theory,Designs, Codes and CryptographyandFinite Fields and Their Applications. In 2017 and 2019, he was selected to Hubei Chutian Scholar Program and Hubei Hundred Scholars Program, respectively.
Wang Mingqiang, professor at the School of Mathematics
October 8 (Saturday) 10:00-11:00,