A new family of arrays with low autocorrelation

作者：Dietrich Heiko^*; Jolly Nathan

来源：Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences, 2017, 9(6): 737-748.

DOI：10.1007/s12095-017-0214-0

• Almost perfect arrays
• n-perfect arrays
• Periodic autocorrelation
• Recursive constructions

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 x 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 x v and if its autocorrelation array has only n nonzero entries, namely nuv lambda(i) in position (iu, 0) for i = 0, 1,..., n - 1, where lambda 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.

• 出版日期2017-11