Golay Pairs Having Larger Swap Sets
Gregory Emmett Coxson · IEEE Transactions on Aerospace and Electronic Systems · 2020
Binary Golay pairs are examined with an interest in finding examples, in which members of the pair can be replaced with other codes sharing the same autocorrelation, but not due to negation and reversal. These are referred to as shared-autocorrelation (or shared-ACS) Golay pairs. Golay pairs can always formed from other Golay pairs by reversing and/or negating codes in those pairs; the discovery of other possibilities offers the promise of enhanced unpredictability by waveform diversity. A 1998 paper by Djokovic, which lists such pairs at lengths 32 and 40, is used as evidence that such pairs not only exist, but also likely exist in significant numbers. A common structure in these codes is determined, and conditions found for half-codes that can be employed to form larger examples. Furthermore, a necessary condition is found for code lengths allowing these shared-ACS Golay pairs.