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Volume 38, Issue 2
Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

Jun Zhang & Haiyan Zhou

DOI: 10.4208/cmr.2021-0002

Commun. Math. Res., 38 (2022), pp. 206-222.

Published online: 2022-02

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  • 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.

  • Keywords

Finite geometry, finite local ring, Reed-Solomon code, covering radius, deep hole.

  • AMS Subject Headings

11T71, 94B72

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-38-206, author = {Zhang , Jun and Zhou , Haiyan}, title = {Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {38}, number = {2}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0002}, url = {http://global-sci.org/intro/article_detail/cmr/20271.html} }
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 -

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.

Jun Zhang & Haiyan Zhou. (2022). Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings. Communications in Mathematical Research . 38 (2). 206-222. doi:10.4208/cmr.2021-0002
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