On the construction of run permuted sequences

Abstract

This paper describes the construction of classes of binary sequences, which are obtained by permuting the runs of zeroes and ones of some given periodic binary sequence s=(so, s1,…, Sp-1)∞, si∈GF(2). A large class of sequences is constructed by permuting the runs of zeroes and ones of a DeBruijn sequence of given order. The properties of the sequences in this class are discussed. As is known, in this way all DeBruijn sequences of given order are obtained, but also many more sequences with higher complexities, all satisfying Golomb’s first and second randomness postulates. It is shown how to generate the sequences in this class with the use of enumerative coding techniques. A more efficient sequence generator, employing shift registers is also introduced. The binary sequence generator obtained in this way can be useful for cryptographic purposes, e.g. in streamcipher systems.