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