In mathematics, a ±1–sequence is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (x1, x2, x3, ...), where xi = (−1)i+1.
Such sequences are commonly studied in discrepancy theory.
Erdős discrepancy problem
Let S=(x1, x2, x3,...) be a ±1–sequence, where xj denotes the jth term. The Erdős discrepancy problem asks whether there exists a sequence S and an integer CS, such that for any two positive integers d and k,
A Barker code is a sequence of N values of +1 and −1,
- for j = 1, 2, …, N
for all .
- Barker, R. H. (1953). "Group Synchronizing of Binary Digital Sequences". Communication Theory. London: Butterworth. pp. 273–287.
- Chazelle, Bernard. The Discrepancy Method: Randomness and Complexity. Cambridge University Press. ISBN 0-521-77093-9.
- The Erdős discrepancy problem – Polymath Project