PARTIAL DIRECT PRODUCT DIFFERENCE SETS AND ALMOST QUATERNARY SEQUENCES

Ozden B., YAYLA O.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol.17, pp.572-588, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17
  • Publication Date: 2023
  • Doi Number: 10.3934/amc.2021010
  • Journal Name: ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Page Numbers: pp.572-588
  • Keywords: Nearly perfect sequence, partial direct product difference set, quaternary sequence, autocorrelation, cyclotomic classes, BALANCED BINARY SEQUENCES, AUTOCORRELATION, PERFECT, FAMILY
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we study the m-ary sequences with (non-consecutive) two zero-symbols and at most two distinct autocorrelation coefficients, which are known as almost m-ary nearly perfect sequences. We show that these sequences are equivalent to P-partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero symbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for P-PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.