On the existence of cyclic Hadamard difference sets

Jeong Heon Kim; Hong Yeop Song

doi:10.1109/APCC.1999.825007

On the existence of cyclic Hadamard difference sets

Jeong Heon Kim, Hong Yeop Song

Department of Electrical and Electronic Engineering

Research output: Contribution to conference › Paper › peer-review

1 Citation (Scopus)

Abstract

Every known cyclic Hadamard difference set has one of three types of v:(1) v=4n-1 is a prime. (2) v is a product of twin primes. (3) v=2ⁿ-1 for n=2,3,.. It is conjectured that all the cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n<10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and confirmed the conjecture for all vles/3435.

Original language	English
Pages	743-746
Number of pages	4
DOIs	https://doi.org/10.1109/APCC.1999.825007
Publication status	Published - 1998
Event	5th Asia-Pacific Conference Communications and 4th Optoloelectronics Communications Conference, APCC/OECC 1999 - Beijing, China Duration: 1999 Oct 18 → 1999 Oct 22

Other

Other	5th Asia-Pacific Conference Communications and 4th Optoloelectronics Communications Conference, APCC/OECC 1999
Country/Territory	China
City	Beijing
Period	99/10/18 → 99/10/22

Bibliographical note

Funding Information:
This work is part of research supported by University Research Program of “Ministry of Information Communication in South Korea”.

Publisher Copyright:
© 1999 China Inst. Of Communications.

All Science Journal Classification (ASJC) codes

Hardware and Architecture
Electrical and Electronic Engineering
Communication
Computer Networks and Communications

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10.1109/APCC.1999.825007

Cite this

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title = "On the existence of cyclic Hadamard difference sets",

abstract = "Every known cyclic Hadamard difference set has one of three types of v:(1) v=4n-1 is a prime. (2) v is a product of twin primes. (3) v=2n-1 for n=2,3,.. It is conjectured that all the cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n<10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and confirmed the conjecture for all vles/3435.",

author = "Kim, {Jeong Heon} and Song, {Hong Yeop}",

note = "Funding Information: This work is part of research supported by University Research Program of “Ministry of Information Communication in South Korea”. Publisher Copyright: {\textcopyright} 1999 China Inst. Of Communications.; 5th Asia-Pacific Conference Communications and 4th Optoloelectronics Communications Conference, APCC/OECC 1999 ; Conference date: 18-10-1999 Through 22-10-1999",

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doi = "10.1109/APCC.1999.825007",

language = "English",

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T1 - On the existence of cyclic Hadamard difference sets

AU - Kim, Jeong Heon

AU - Song, Hong Yeop

N1 - Funding Information: This work is part of research supported by University Research Program of “Ministry of Information Communication in South Korea”. Publisher Copyright: © 1999 China Inst. Of Communications.

PY - 1998

Y1 - 1998

N2 - Every known cyclic Hadamard difference set has one of three types of v:(1) v=4n-1 is a prime. (2) v is a product of twin primes. (3) v=2n-1 for n=2,3,.. It is conjectured that all the cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n<10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and confirmed the conjecture for all vles/3435.

AB - Every known cyclic Hadamard difference set has one of three types of v:(1) v=4n-1 is a prime. (2) v is a product of twin primes. (3) v=2n-1 for n=2,3,.. It is conjectured that all the cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n<10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and confirmed the conjecture for all vles/3435.

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DO - 10.1109/APCC.1999.825007

M3 - Paper

AN - SCOPUS:80955137153

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EP - 746

T2 - 5th Asia-Pacific Conference Communications and 4th Optoloelectronics Communications Conference, APCC/OECC 1999

Y2 - 18 October 1999 through 22 October 1999

ER -

On the existence of cyclic Hadamard difference sets

Abstract

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Bibliographical note

All Science Journal Classification (ASJC) codes

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