New Optimal Difference Systems of Sets from Ideal Sequences and Perfect Ternary Sequences

Yong WANG  Wei SU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.5   pp.792-797
Publication Date: 2020/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAL2144
Type of Manuscript: LETTER
Category: Coding Theory
difference systems of sets,  ideal sequences,  perfect sequences,  difference balanced property,  d-form property,  

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Difference systems of sets (DSSs) introduced by Levenstein are combinatorial structures used to construct comma-free codes for synchronization. In this letter, two classes of optimal DSSs are presented. One class is obtained based on q-ary ideal sequences with d-form property and difference-balanced property. The other class of optimal and perfect DSSs is derived from perfect ternary sequences given by Ipatov in 1995. Compared with known constructions (Zhou, Tang, Optimal and perfect difference systems of sets from q-ary sequences with difference-balanced property, Des. Codes Cryptography, 57(2), 215-223, 2010), the proposed DSSs lead to comma-free codes with nonzero code rate.