Random Matrices from Linear Codes and Wigner's Semicircle Law II

Chin Hei Chan; Maosheng Xiong

doi:10.1109/IWSDA46143.2019.8966107

Random Matrices from Linear Codes and Wigner's Semicircle Law II

Chin Hei Chan, Maosheng Xiong

Department of Mathematics

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

3 Citations (Scopus)

Abstract

Recently we considered a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and proved that under some natural algebraic conditions their empirical spectral distribution converges to Wigner's semicircle law as the length of the codes goes to infinity. One of the conditions is that the dual distance of the codes is at least 5. In this report, by employing more advanced techniques related to Stieltjes transform, we show that the dual distance being at least 5 is sufficient to ensure the convergence. We also obtain a fast convergence rate in terms of the length of the code.

Original language	English
Title of host publication	2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728116693
DOIs	https://doi.org/10.1109/IWSDA46143.2019.8966107
Publication status	Published - Oct 2019
Event	9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019 - Dongguan, China Duration: 20 Oct 2019 → 24 Oct 2019

Publication series

Name	2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019

Conference

Conference	9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019
Country/Territory	China
City	Dongguan
Period	20/10/19 → 24/10/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

Group randomness
Wigner's semicircle law
dual distance
empirical spectral measure
linear code
random matrix theory

Access to Document

10.1109/IWSDA46143.2019.8966107

Cite this

Chan, C. H., & Xiong, M. (2019). Random Matrices from Linear Codes and Wigner's Semicircle Law II. In 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019 Article 8966107 (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IWSDA46143.2019.8966107

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title = "Random Matrices from Linear Codes and Wigner's Semicircle Law II",

abstract = "Recently we considered a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and proved that under some natural algebraic conditions their empirical spectral distribution converges to Wigner's semicircle law as the length of the codes goes to infinity. One of the conditions is that the dual distance of the codes is at least 5. In this report, by employing more advanced techniques related to Stieltjes transform, we show that the dual distance being at least 5 is sufficient to ensure the convergence. We also obtain a fast convergence rate in terms of the length of the code.",

keywords = "Group randomness, Wigner's semicircle law, dual distance, empirical spectral measure, linear code, random matrix theory",

author = "Chan, \{Chin Hei\} and Maosheng Xiong",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019 ; Conference date: 20-10-2019 Through 24-10-2019",

year = "2019",

month = oct,

doi = "10.1109/IWSDA46143.2019.8966107",

language = "English",

series = "2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019",

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booktitle = "2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019",

}

Chan, CH & Xiong, M 2019, Random Matrices from Linear Codes and Wigner's Semicircle Law II. in 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019., 8966107, 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019, Institute of Electrical and Electronics Engineers Inc., 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019, Dongguan, China, 20/10/19. https://doi.org/10.1109/IWSDA46143.2019.8966107

Random Matrices from Linear Codes and Wigner's Semicircle Law II. / Chan, Chin Hei; Xiong, Maosheng.
2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8966107 (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019).

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

TY - GEN

T1 - Random Matrices from Linear Codes and Wigner's Semicircle Law II

AU - Chan, Chin Hei

AU - Xiong, Maosheng

PY - 2019/10

Y1 - 2019/10

N2 - Recently we considered a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and proved that under some natural algebraic conditions their empirical spectral distribution converges to Wigner's semicircle law as the length of the codes goes to infinity. One of the conditions is that the dual distance of the codes is at least 5. In this report, by employing more advanced techniques related to Stieltjes transform, we show that the dual distance being at least 5 is sufficient to ensure the convergence. We also obtain a fast convergence rate in terms of the length of the code.

AB - Recently we considered a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and proved that under some natural algebraic conditions their empirical spectral distribution converges to Wigner's semicircle law as the length of the codes goes to infinity. One of the conditions is that the dual distance of the codes is at least 5. In this report, by employing more advanced techniques related to Stieltjes transform, we show that the dual distance being at least 5 is sufficient to ensure the convergence. We also obtain a fast convergence rate in terms of the length of the code.

KW - Group randomness

KW - Wigner's semicircle law

KW - dual distance

KW - empirical spectral measure

KW - linear code

KW - random matrix theory

UR - https://openalex.org/W3001726001

UR - https://www.scopus.com/pages/publications/85079214669

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DO - 10.1109/IWSDA46143.2019.8966107

M3 - Conference Paper published in a book

T3 - 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019

BT - 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019

Y2 - 20 October 2019 through 24 October 2019

ER -

Chan CH, Xiong M. Random Matrices from Linear Codes and Wigner's Semicircle Law II. In 2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019. Institute of Electrical and Electronics Engineers Inc. 2019. 8966107. (2019 9th International Workshop on Signal Design and its Applications in Communications, IWSDA 2019). doi: 10.1109/IWSDA46143.2019.8966107

Random Matrices from Linear Codes and Wigner's Semicircle Law II

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Keywords

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