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编码密码学术活动月系列活动二

发布日期:2020-10-05点击量:

报告题目:How many weights can a quasi-cyclic code have ?

报告人:施敏加 教授(安徽大学)

报告时间:2020年10月7日下午14:00-15:00

摘要:We investigate the largest number of nonzero weights of quasi-cyclic codes. In particular, we focus on the function $\Gamma_Q(n,\ell,k,q),$ that is defined to be the largest number of nonzero weights a quasi-cyclic code of index $\gcd(\ell,n)$, length $n$ and dimension $k$ over $\Fq$ can have, and connect it to similar functions related to linear and cyclic codes. We provide several upper and lower bounds on this function, using different techniques and studying its asymptotic behavior. Moreover, we determine the smallest index for which a $q$-ary Reed-Muller code is quasi-cyclic, a result of independent interest.


报告题目:Binary sequences with low odd correlation

报告人:杨洋 副教授(西南交通大学)

报告时间:2020年10月7日下午15:00-16:00

摘要:In this talk, using the interleaving technique, we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation. As a result, some new binary sequences/sequences sets with optimal odd auto-correlation magnitude are obtained.


报告题目:A bound on the minimum distance of generalized quasi-twisted codes

报告人:高健 副教授(山东理工大学)

报告时间:2020年10月7日下午16:00-17:00

摘要:Generalized quasi-twisted (GQT) codes form a generalization of quasi-twisted (QT) codes and generalized quasi-cyclic (GQC) codes. By the Chinese remainder theorem, the GQT codes can be decomposed into a direct sum of some linear codes over Galois extension fields, which leads to the trace representation of the GQT codes. Using this trace representation, we first prove the minimum distance bound for GQT codes with two constituents. Then we generalize the result to GQT codes with s constituents. Finally, we present some examples to show that the bound is better than the well-known Esmaeili-Yari bound and sharp in many instances.


腾讯会议号:812 998 799

联系人:张俊

主办单位:首都师范大学数学科学学院、万博体育max手机登陆app-手机版下载