Year: 2022
Author: Jun Zhang, Haiyan Zhou
Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 206–222
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0002
Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 206–222
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Finite geometry finite local ring Reed-Solomon code covering radius deep hole.
Author Details
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The deep hole 问题 of generalized Reed-Solomon codes
Jun, Zhang
Haiyan, Zhou
SCIENTIA SINICA Mathematica, Vol. 53 (2023), Iss. 11 P.1409
https://doi.org/10.1360/SSM-2023-0118 [Citations: 0]