Abstract
Arrays with low autocorrelation are widely sought in applications; important examples are arrays whose periodic autocorrelation is zero for all nontrivial cyclic shifts, so-called perfect arrays. In 2001, Arasu and de Launey defined almost perfect arrays: these have size 2u×v and autocorrelation arrays with only two nonzero entries, namely 2uv and −2uv in positions (0,0) and (u,0), respectively. In this paper we present a new class of arrays with low autocorrelation: for an integer n≥1, we call an array n-perfect if it has size nu×v and if its autocorrelation array has only n nonzero entries, namely nuvλi in position (iu,0) for i=0,1,…,n−1, where λ is a primitive n-th root of unity. Thus, an array is 1-perfect (2-perfect) if and only if it is (almost) perfect. We give examples and describe a recursive construction of families of n-perfect arrays of increasing size.
| Original language | English |
|---|---|
| Pages (from-to) | 737-748 |
| Number of pages | 12 |
| Journal | Cryptography and Communications: discrete structures, Boolean functions and sequences |
| Volume | 9 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
Keywords
- Almost perfect arrays
- n-perfect arrays
- Periodic autocorrelation
- Recursive constructions
Cite this
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A new family of arrays with low autocorrelation. / Dietrich, Heiko; Jolly, Nathan.
In: Cryptography and Communications: discrete structures, Boolean functions and sequences, Vol. 9, No. 6, 01.11.2017, p. 737-748.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - A new family of arrays with low autocorrelation
AU - Dietrich, Heiko
AU - Jolly, Nathan
PY - 2017/11/1
Y1 - 2017/11/1
N2 - Arrays with low autocorrelation are widely sought in applications; important examples are arrays whose periodic autocorrelation is zero for all nontrivial cyclic shifts, so-called perfect arrays. In 2001, Arasu and de Launey defined almost perfect arrays: these have size 2u×v and autocorrelation arrays with only two nonzero entries, namely 2uv and −2uv in positions (0,0) and (u,0), respectively. In this paper we present a new class of arrays with low autocorrelation: for an integer n≥1, we call an array n-perfect if it has size nu×v and if its autocorrelation array has only n nonzero entries, namely nuvλi in position (iu,0) for i=0,1,…,n−1, where λ is a primitive n-th root of unity. Thus, an array is 1-perfect (2-perfect) if and only if it is (almost) perfect. We give examples and describe a recursive construction of families of n-perfect arrays of increasing size.
AB - Arrays with low autocorrelation are widely sought in applications; important examples are arrays whose periodic autocorrelation is zero for all nontrivial cyclic shifts, so-called perfect arrays. In 2001, Arasu and de Launey defined almost perfect arrays: these have size 2u×v and autocorrelation arrays with only two nonzero entries, namely 2uv and −2uv in positions (0,0) and (u,0), respectively. In this paper we present a new class of arrays with low autocorrelation: for an integer n≥1, we call an array n-perfect if it has size nu×v and if its autocorrelation array has only n nonzero entries, namely nuvλi in position (iu,0) for i=0,1,…,n−1, where λ is a primitive n-th root of unity. Thus, an array is 1-perfect (2-perfect) if and only if it is (almost) perfect. We give examples and describe a recursive construction of families of n-perfect arrays of increasing size.
KW - Almost perfect arrays
KW - n-perfect arrays
KW - Periodic autocorrelation
KW - Recursive constructions
UR - http://www.scopus.com/inward/record.url?scp=85026908299&partnerID=8YFLogxK
U2 - 10.1007/s12095-017-0214-0
DO - 10.1007/s12095-017-0214-0
M3 - Article
VL - 9
SP - 737
EP - 748
JO - Cryptography and Communications: discrete structures, Boolean functions and sequences
JF - Cryptography and Communications: discrete structures, Boolean functions and sequences
SN - 1936-2447
IS - 6
ER -