New Optimal Difference Systems of Sets from Ideal Sequences and Perfect Ternary Sequences
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.5 pp.792-797
- Publication Date
- 2020/05/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2019EAL2144
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Keyword
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Yong WANG, Wei SU, "New Optimal Difference Systems of Sets from Ideal Sequences and Perfect Ternary Sequences" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 5, pp. 792-797, May 2020, doi: 10.1587/transfun.2019EAL2144.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAL2144/_p
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@ARTICLE{e103-a_5_792,
author={Yong WANG, Wei SU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Optimal Difference Systems of Sets from Ideal Sequences and Perfect Ternary Sequences},
year={2020},
volume={E103-A},
number={5},
pages={792-797},
abstract={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.},
keywords={},
doi={10.1587/transfun.2019EAL2144},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - New Optimal Difference Systems of Sets from Ideal Sequences and Perfect Ternary Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 792
EP - 797
AU - Yong WANG
AU - Wei SU
PY - 2020
DO - 10.1587/transfun.2019EAL2144
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2020
AB - 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.
ER -
English
