Constructions of Complementary Sequence Sets and Complete Complementary Codes by Ideal Two-Level Autocorrelation Sequences and Permutation Polynomials

Wang, Zilong; Gong, Guang

doi:10.1109/tit.2023.3258180

Cited by 6 publications

(2 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In general, many kinds of sequence sets with orthogonal properties are basically constructed using complex Hadamard matrices, so the construction methods of complementary sets, such as ZCZ codes [12]- [14] and the Reed-Muller code [15], [16], are closely related. In particular, the construction methods of complementary sequence sets were discussed by using generalized Boolean functions, which can uniquely express the generated sequences, so that the difference between the sequence sets can be clarified and their characteristics and relevance to ZCZ codes and Reed-Muller codes were clarified [17], [19]. Previously, the authors also derived the logic functions of some ZCZ codes and showed their differences [20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Logic Functions of Polyphase Complementary Sets

MATSUFUJI,

KURODA,

IDA

et al. 2023

IEICE Trans. Fundamentals

View full text Add to dashboard Cite

A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K , M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(N n , N , N ) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.

show abstract

Section: Introductionmentioning

confidence: 99%

“…[23]. The logic function is the same as the generalized Boolean function except that it allows mapping to the real numbers modulo integer q, since even if the logic function includes real-valued functions and irrational numbers, it can be handled well [25]- [28] This discussion will be closely related to references [17]- [19].…”

Section: Introductionmentioning

confidence: 99%