Cuiling Fan

Constructing bent functions and bent idempotents of any possible algebraic degrees

2015 · arXiv (Cornell University)

Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the …

Roth–Lempel NMDS Codes of Non-Elliptic-Curve Type

2023 · IEEE Transactions on Information Theory

The defect of an$[n,k,d]$linear code is defined as$s({\mathcal{ C}})=n-k+1-d$. Codes with$s({\mathcal{ C}})=0$are called maximum distance separable (MDS), while codes with$s({\mathcal{ C}})=s({\mathcal{ C}}^{\perp})=1$are called near maximum distance separable (NMDS). NMDS codes correspond to interesting objects in …

Combinatorial $t$-Designs from Finite Abelian Groups and Their Applications to Elliptic Curve Codes

2025 · arXiv (Cornell University)

In this paper, we establish the conditions for some finite abelian groups and the family all the $k$-sets in each of them summing up to an element $x$ to form $t$-designs. We fully characterize the …