Ramakrishna Bandi

In this paper, we present an isomorphism that connects a code of length [ ] over [ ] to a code of length [ ] over [ ]. We define criteria for identifying linear complementary pair (LCP) and linear complementary dual (LCD) codes by utilizing this isomorphism. We also introduce the notion of [ ]-LCP of codes into the LCP framework and give a necessary and sufficient condition for their characterization. We also provide a necessary and sufficient condition for the existence of an maximum distance separable (MDS) [ ]-LCP of codes. These insights into the structural properties of codes offer promising avenues for their application in various fields, particularly in the realm of finite fields.

A verifiable multi-secret sharing (VMSS) scheme addresses various security issues, helping in cheating detection and cheater identification. The dimension of the intersection of a given pair of cyclic codes over a finite field [ ] is represented by [ ]. In this paper, we propose a VMSS scheme based on an [ ]-intersection pair of cyclic codes. The proposed scheme is very useful for sharing a large number of secrets. If [ ] is the number of secrets in a threshold [ ] scheme, then for [ ], the computational complexity and the public values required in the reconstruction phase are much less compared to many existing schemes in the literature. Overall, the proposed scheme comprises nearly all the features, like being verifiable, testing participants’ integrity, checking Verifier frauds, and most importantly, it is of multi-use type.