By Topic

A Framework for the Construction ofGolay Sequences

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Frank Fiedler ; Dept. of Math., Wesley Coll., Dover, DE ; Jonathan Jedwab ; Matthew G. Parker

In 1999, Davis and Jedwab gave an explicit algebraic normal form for m!/2 - 2h(m+1) ordered Golay pairs of length 2mmiddot over Z2h, involving m!/2 - 2h(m+1) Golay sequences. In 2005, Li and Chu unexpectedly found an additional 1024 length 16 quaternary Golay sequences. Fiedler and Jedwab showed in 2006 that these new Golay sequences exist because of a "crossover" of the aperiodic autocorrelation function of certain quaternary length eight sequences belonging to Golay pairs, and that they spawn further new quaternary Golay sequences and pairs of length 2m for m > 4 under Budisin's 1990 iterative construction. The total number of Golay sequences and pairs spawned in this way is counted, and their algebraic normal form is given explicitly. A framework of constructions is derived in which Turyn's 1974 product construction, together with several variations, plays a key role. All previously known Golay sequences and pairs of length 2m over Z2h can be obtained directly in explicit algebraic normal form from this framework. Furthermore, additional quaternary Golay sequences and pairs of length 2m are produced that cannot be obtained from any other known construction. The framework generalizes readily to lengths that are not a power of 2, and to alphabets other than Z2h .

Published in:

IEEE Transactions on Information Theory  (Volume:54 ,  Issue: 7 )