New Families of Binary Sequence Pairs With Two-Level and Three-Level Correlation

Abstract

A pair of binary sequences is generalized from the concept of a two-level autocorrelation function of a single binary sequence. In this paper, new families of binary sequence pairs with period , where gcd , and optimal correlation values are constructed, as well as new families of binary sequence pairs with three-level correlation and period . For the new binary sequence pairs with optimal correlation values, their corresponding new difference set pairs and almost difference set pairs are also derived.Index Terms-Almost difference set pair (ADSP), binary sequence pair, difference set pair (DSP), optimal correlation value.

Constructing Longer Sequences Using a New Improved Interleaved Structure

“…For example, some binary sequences defined on {0, 1} [6] [called as (0, 1) binary sequence], some other binary sequences defined on {1, −1} [called as (1, −1) binary sequences], ternary sequences take only three values {1, 0, −1} [2], q-ary sequences are usually defined on a q-size alphabet with selected complex values [3,5].…”

“…If sequences x and y are (0, 1)-binary sequences, the periodic cross-correlation function between sequence x and y is defined as (2) [6]:…”

“…Sequences with γ = 0 are called as perfect sequences, whereas those with γ = −1 are called as ideal sequences [6].…”

“…Inspired by the interleaved structure proposed in [6], we proposed an enhanced interleaved structure as follows. Here gcd(n, p) = 1 is assumed.…”

“…Although having been a long standing hot topic in the literature, research on construction method for sequences with desired properties is still an active topic and is of key importance. Recently, the authors of [6] proposed a new interesting interleaving structure and then proposed several new methods for constructing longer (0, 1) binary sequence pairs with ideal two-level and three-level correlation values from shorter ideal binary sequences.…”