Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

Jun Zhang

Haiyan Zhou

  1. 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]