Partial direct product difference sets and sequences with ideal autocorrelation

2020/05/26 by Büşra Özden, Özden, Büşra, Oğuz Yayla +1
Computer Science · Engineering · #05B10 #94A55 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Wireless Communication Networks Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2005.12497

openalex publication_date 2020/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the sequences with (non-consecutive) two zero-symbols and ideal autocorrelation, which are also known as almost m-ary nearly perfect sequences. We show that these sequences are equivalent to ℓ-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 ℓ-PDPDS. Finally, we present a construction method for a family of almost quaternary sequences with ideal autocorrelation by using cyclotomic classes.

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