Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings (Communications in Mathematical Research, 2022)
In this paper, we first propose the maximum arc problem, normalrational curve conjecture, and extensions of normal rational curves over finitelocal rings, analogously to the finite geometry over finite fields. We then studythe deep hole problem of generalized Reed-Solomon (RS) codes over finite localrings. Several different classes of deep holes are constructed. The relationshipbetween finite geometry and deep holes of RS codes over finite local rings arealso studied.