Small Golay sequences

Frank Fiedler

doi:10.3934/amc.2013.7.379

Article Contents

2013, Volume 7, Issue 4: 379-407. Doi: 10.3934/amc.2013.7.379

This issue Previous Article Next Article The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$

Small Golay sequences

Frank Fiedler^1,

1.
Wesley College, 120 N State St, Dover, DE 19901

Received: December 2010

Revised: July 2013

Published: November 2013

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Abstract

We enumerate $H$-phase Golay sequences for $H\le 36$ and lengths up to 33. Our enumeration method is based on filtering by the power spectra. Some of the hexaphase Golay sequence pairs are new. We provide a compact way to reconstruct all these Golay sequences from specific Golay arrays. The Golay arrays are part of the three-stage construction introduced by Fiedler, Jedwab, and Parker. All such minimal Golay arrays can be constructed from a small set of Golay sequence pairs with binary, quaternary, or hexaphase alphabet adjoining 0. We also prove some non-existence results for Golay sequences when $H/2$ is odd.

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Mathematics Subject Classification: Primary: 94A55, 68P30; Secondary: 05A15.

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References

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