Abstract-In this paper, we study a class of twisted generalized Reed-Solomon (TGRS) codes with general$\ell$twists. A sufficient and necessary condition for the TGRS codes to be MDS or$\ell$-MDS$(\ell < \min \{k, n-k\})$is determined. A sufficient and necessary condition that such a TGRS code is self-dual for$\ell \leq\left\lfloor\frac{k-1}{3}\right\rfloor$is also presented. Finally, we give an explicit construction of self-dual TGRS codes.

List-decoding and average-radius list-decoding are important generalizations of unique decoding that received considerable attention over the years. However, the optimal trade-off among list-decoding radius, list size, and the code rate are not fully understood in both problems. In this paper, firstly, we prove a new Singleton-type bound for list-decodability, which improves the results of [3]. Next, we prove a Singleton-type bound for average-radius list-decodable codes, which is to the best of our knowledge, the first such bound for average-radius list-decodable codes.