Shared-Autocorrelation Binary Codes Found by Exhaustive Search
Gregory Emmett Coxson, Jon Carmelo Russo · IEEE Transactions on Aerospace and Electronic Systems · 2019
Binary code negation and reversal are known to leave the autocorrelation sequence (ACS) unchanged. However, for some code lengths, there exist “shared-autocorrelation” code pairs for which the mechanism behind shared autocorrelation is not so simple. In this paper, exhaustive search is used to find representatives for all such code pairs for lengths 2 to 39. The resulting code pairs are used to discover code structures associated with the shared autocorrelation property. Some of the code pairs discovered exhibit either Golay skew-symmetry or are found to be Kronecker products of smaller shared-autocorrelation pairs. All four-code sets (or quads) for length N ≤ 36 having the shared-ACS property were also found.