TY - JOUR
T1 - Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings
AU - Zhang , Jun
AU - Zhou , Haiyan
JO - Communications in Mathematical Research 
VL - 2
SP - 206
EP - 222
PY - 2022
DA - 2022/02
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0002
UR - https://global-sci.org/intro/article_detail/cmr/20271.html
KW - Finite geometry, finite local ring, Reed-Solomon code, covering radius, deep hole.
AB - <p style="text-align: justify;">In this paper, we first propose the maximum arc problem, normal
rational curve conjecture, and extensions of normal rational curves over finite
local rings, analogously to the finite geometry over finite fields. We then study
the deep hole problem of generalized Reed-Solomon (RS) codes over finite local
rings. Several different classes of deep holes are constructed. The relationship
between finite geometry and deep holes of RS codes over finite local rings are
also studied.</p>