±1-sequence

# ±1-sequence

Discussion

Encyclopedia
In mathematics, a ±1–sequence, (x1, x2, x3, ...), is a sequence
Sequence
In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...

where each xi is one of {1, −1}.

Such sequences are commonly studied in discrepancy theory
Discrepancy theory
In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be. It is also called theory of irregularities of distribution. This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly...

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## 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,

, this problem is currently being studied by the Polymath project.

## Barker Codes

A Barker code is a sequence of N values of +1 and −1, for j = 1, 2, …, N
such that
for all .

Barker codes of length 11 and 13 are used in direct-sequence spread spectrum