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Distance Distribution in Reed-Solomon Codes.
- Source :
- IEEE Transactions on Information Theory; May2020, Vol. 66 Issue 5, p2743-2750, 8p
- Publication Year :
- 2020
-
Abstract
- Let $\mathbb {F}_{q}$ be the finite field of $q$ elements. In this paper we obtain bounds on the following counting problem: given a polynomial $f(x)\in \mathbb {F}_{q} [x]$ of degree $k+m$ and a non-negative integer $r$ , count the number of polynomials $g(x)\in \mathbb {F}_{q} [x]$ of degree at most $k-1$ such that $f(x)+g(x)$ has exactly $r$ roots in $\mathbb {F}_{q}$. Previously, explicit formulas were known only for the cases $m=0, 1, 2$. As an application, we obtain an asymptotic formula on the list size of the standard Reed-Solomon code $[q, k, q-k+1]_{q}$. [ABSTRACT FROM AUTHOR]
- Subjects :
- REED-Solomon codes
FINITE fields
LINEAR codes
POLYNOMIALS
INTEGERS
DISTANCES
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 143315415
- Full Text :
- https://doi.org/10.1109/TIT.2019.2933625