Asymptotic Normality of Q-Ary Linear Codes

Minjia Shi; Olivier Rioul; Patrick Sole

doi:10.1109/LCOMM.2019.2935729

Asymptotic Normality of Q-Ary Linear Codes

Minjia Shi, Olivier Rioul, Patrick Sole

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

Abstract

Sidel'nikov proved in 1971 that the weight distribution of long binary codes is asymptotically Gaussian. Delsarte sketched in 1975 an extension of this result to Q -ary codes when Q > 2. In this note, we complete Delsarte's proof.

Original language	English
Article number	8804213
Pages (from-to)	1895-1898
Number of pages	4
Journal	IEEE Communications Letters
Volume	23
Issue number	11
DOIs	https://doi.org/10.1109/LCOMM.2019.2935729
Publication status	Published - 1 Nov 2019
Externally published	Yes

Keywords

Berry's inequality
Linear codes
weight distribution

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10.1109/LCOMM.2019.2935729

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title = "Asymptotic Normality of Q-Ary Linear Codes",

abstract = "Sidel'nikov proved in 1971 that the weight distribution of long binary codes is asymptotically Gaussian. Delsarte sketched in 1975 an extension of this result to Q -ary codes when Q > 2. In this note, we complete Delsarte's proof.",

keywords = "Berry's inequality, Linear codes, weight distribution",

author = "Minjia Shi and Olivier Rioul and Patrick Sole",

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AB - Sidel'nikov proved in 1971 that the weight distribution of long binary codes is asymptotically Gaussian. Delsarte sketched in 1975 an extension of this result to Q -ary codes when Q > 2. In this note, we complete Delsarte's proof.

KW - Berry's inequality

KW - Linear codes

KW - weight distribution

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DO - 10.1109/LCOMM.2019.2935729

M3 - Article

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EP - 1898

JO - IEEE Communications Letters

JF - IEEE Communications Letters

IS - 11

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Asymptotic Normality of Q-Ary Linear Codes

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Keywords

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