Exploring strong controlled partial metric type spaces: Analysis of fixed points and theoretical contributions.

This study involves the generalization of partial metric spaces and strong controlled metric type spaces through the introduction of the notion of strong controlled partial metric type spaces. This research pursues a dual objective: firstly, to scrutinize fixed points related to contractions of the Kannan type within the framework of strong controlled partial metric type spaces, encompassing both linear and nonlinear contractions; secondly, to furnish illustrative examples and applications that underscore the consequential implications of our theoretical contributions.

On Optimal and Quantum Code Construction from Cyclic Codes over F with Applications.

The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3-α22v⟩ and Q=Fq[u,v]⟨u2-α12,v3-α22v⟩ are nonchain finite rings and αi is in Fq/{0} for i∈{1,2}, where q=pm with m≥1 is a positive integer and is an odd prime. Moreover, with the applications, we obtain better and new quantum error-correcting (QEC) codes. For another application over the ring , we obtain several optimal codes with the help of the Gray image of cyclic codes.