A note on the Newton radius

Alex Samorodnitsky; Sergey Yekhanin

doi:10.1016/j.disc.2012.03.038

A note on the Newton radius

Alex Samorodnitsky, Sergey Yekhanin

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

The Newton radius of a code is the largest weight of a uniquely correctable error. We establish a lower bound for the Newton radius in terms of the rate. In particular we show that in any family of linear codes of rate below one half, the Newton radius increases linearly with the codeword length.

Original language	English
Pages (from-to)	2392-2393
Number of pages	2
Journal	Discrete Mathematics
Volume	312
Issue number	15
DOIs	https://doi.org/10.1016/j.disc.2012.03.038
State	Published - 6 Aug 2012

Keywords

68P30
Covering radius
Newton radius

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2012.03.038

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title = "A note on the Newton radius",

abstract = "The Newton radius of a code is the largest weight of a uniquely correctable error. We establish a lower bound for the Newton radius in terms of the rate. In particular we show that in any family of linear codes of rate below one half, the Newton radius increases linearly with the codeword length.",

keywords = "68P30, Covering radius, Newton radius",

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year = "2012",

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doi = "10.1016/j.disc.2012.03.038",

language = "الإنجليزيّة",

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AB - The Newton radius of a code is the largest weight of a uniquely correctable error. We establish a lower bound for the Newton radius in terms of the rate. In particular we show that in any family of linear codes of rate below one half, the Newton radius increases linearly with the codeword length.

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U2 - 10.1016/j.disc.2012.03.038

DO - 10.1016/j.disc.2012.03.038

M3 - مقالة

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SP - 2392

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 15

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A note on the Newton radius

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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