Compatible difference packing set systems and their applications to multilength variable-weight OOCs

In a study of multilength variable-weight optical orthogonal codes (MLVWOOCs), compatible ( N ,  M ,  W , 1,  Q ; 2) difference packing (briefly ( N ,  M ,  W , 1,  Q ; 2)-CDP) set systems play an important role. In this paper, a new consequence of Weil’s theorem on multiplicative character sums is...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2022-11, Vol.90 (11), p.2613-2645
Main Authors: Qin, Rongcun, Zhao, Hengming, Yu, Huangsheng
Format: Article
Language:English
Subjects:
Coding and Information Theory
Compatibility
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless
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Summary:In a study of multilength variable-weight optical orthogonal codes (MLVWOOCs), compatible ( N ,  M ,  W , 1,  Q ; 2) difference packing (briefly ( N ,  M ,  W , 1,  Q ; 2)-CDP) set systems play an important role. In this paper, a new consequence of Weil’s theorem on multiplicative character sums is presented, some direct constructions of pairwise 2-compatible balanced ( n ,  g ,  W , 1) difference families (DFs) are obtained for W = { 3 , 4 } , { 3 , 5 } , and recursive constructions for ( N ,  M ,  W , 1,  Q ; 2)-CDP set systems are derived by means of semicyclic group divisible designs (SCGDDs). Some series of compatible difference packing set systems are produced, and several infinite classes of optimal MLVWOOCs are then obtained.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-021-00927-y