Extension of quadratic residue codes and the minimal distance

 报告题目:  Extension of quadratic residue codes and the minimal distance

 报  告  人:熊茂胜    副教授(香港科技大学,数学系)




In an interesting paper Professor Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and dimension over the same finite field. However, not much is known about these codes. In this work we explain some of the mysteries of the numerical data by developing a general method on cyclic codes of composite length and on estimating the minimal distance. Inspired by the method, we also provide a general construction of cyclic codes of composite length. Numerical data shows that it produces many best cyclic codes as well. Finally, we point out how these cyclic codes can be used to construct convolutional codes with large free distance.


Maosheng Xiong received the Ph.D. degree in mathematics from University of Illinois at Urbana-Champaign in 2007. He was a postdoc at Pennsylvania State University from August 2007 to June 2010.He joined the Department of Mathematics, the Hong Kong University of Science and Technology in July 2010 and is currently an associate professor. His area of research interests is in algebraic coding theory and number theory.