NDLI: Existence of cyclic Hadamard difference sets and its relation to binary sequences with ideal autocorrelation

Content Provider	IEEE Xplore Digital Library
Author	Kim, Jeong-Heon Song, Hong-Yeop
Copyright Year	2011
Abstract	Balanced binary sequences with ideal autocorrelation are equivalent to (v, k, λ)-cyclic Hadamard difference sets with v = 4n − 1, k = 2n − 1, λ = n − 1 for some positive integer n. Every known cyclic Hadamard difference set has one of the following 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 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 the conjecture is confirmed for all v ≤ 3435. In addition, all the inequivalent cyclic Hadamard difference sets with v = 2ⁿ − 1 for n ≤ 10 are listed and classified according to known construction methods.
Starting Page	14
Ending Page	18
Page Count	5
File Size	209030
File Format	PDF
ISSN	12292370
Volume Number	1
Issue Number	1
Language	English
Publisher	Editorial Department of Journal of Communications and Networks
Publisher Date	1999-03-01
Publisher Place	South Korea
Access Restriction	Subscribed
Rights Holder	JCN
Subject Keyword	Correlation Equations Educational institutions Multiaccess communication Error correction Error correction codes Presses Cyclic Hadamard Difference Sets Pseudorandom Binary Sequences Ideal Autocorrelation
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Information Systems

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