p-ary unified sequences: p-ary extended d-form sequences with the ideal autocorrelation property

In this paper, for a prime number p, a construction method to generate p-ary d-form sequences with the ideal autocorrelation property is proposed and using the ternary sequences found by Helleseth, Kumar, and Martinsen (2000), ternary d-form sequences with the ideal autocorrelation property are constructed. By combining the methods for generating p-ary extended sequences (a special case of geometric sequences) and p-ary d-form sequences, a construction method of p-ary unified (extended d-form) sequences which also have the ideal autocorrelation property is proposed. This is a very general class of p-ary sequences including the binary and nonbinary extended sequences and the d-form sequences. From the ternary sequences by Helleseth, Kumar, and Martinsen, ternary unified sequences with the ideal autocorrelation property are also generated.