The decimation-Hadamard transform of two-level autocorrelation sequences

A new method to study and search for two-level autocorrelation sequences for both binary and nonbinary cases is developed. This method iteratively applies two operations: decimation and the Hadamard transform based on general orthogonal functions, referred to as the decimation-Hadamard transform (DHT). The second iterative DHT can transform one class of such sequences into another inequivalent class of such sequences, a process called realization. The existence and counting problems of the second iterative DHT are discussed. Using the second iterative DHT, and starting with a single binary -sequence (when is odd), we believe one can obtain all the known two-level autocorrelation sequences of period 2 1 which have no subfield factorization. We have verified this for odd 17. Interestingly, no previously unknown examples were found by this process for any odd 17. This is supporting evidence (albeit weak) for the conjecture that all families of cyclic Hadamard difference sets of period 2 1...

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Guang Gong, Solomon W. Golomb
• Keywords: General Orthogonal Functions, Iterative Dht, TIT 2002, Two-level Autocorrelation Sequences