# Generalized binary arrays from quasi-orthogonal cocycles

## TL;DR

This paper introduces generalized optimal binary arrays (GOBAs) with specific energy properties, providing a construction method based on 2-cocycles and applying it to find negaperiodic Golay pairs from small-length sequences.

## Contribution

It extends the concept of perfect binary arrays by defining GOBAs with new energy conditions and offers a construction method using 2-cocycles, also identifying related Golay pairs.

## Key findings

- GOBAs can have even energy not divisible by 4.
- A construction procedure for GOBAs using 2-cocycles is provided.
- Negaperiodic Golay pairs are derived from small-length GOBAs.

## Abstract

Generalized perfect binary arrays (GPBAs) were used by Jedwab to construct perfect binary arrays. A non-trivial GPBA can exist only if its energy is $2$ or a multiple of $4$. This paper introduces generalized optimal binary arrays (GOBAs) with even energy not divisible by $4$, as analogs of GPBAs. We give a procedure to construct GOBAs based on a characterization of the arrays in terms of $2$-cocycles. As a further application, we determine negaperiodic Golay pairs arising from generalized optimal binary sequences of small length.