Constructions and Applications of Perfect Difference Matrices and Perfect Difference Families
Xianwei Sun, Huangsheng Yu, Dianhua Wu

TL;DR
This paper develops new recursive methods to construct perfect difference matrices and families, significantly expanding their existence range and enabling applications in optical orthogonal codes and radar arrays.
Contribution
It introduces novel recursive constructions for PDM(3,m)s, proving their existence for all odd m<1000 except for known and potential exceptions, and fully characterizes certain perfect difference families.
Findings
PDM(3,m)s exist for all odd m<1000 except 9, 11, and possibly 33.
Complete classification of (g, {3,4}, 1)-PDFs with block size ratio ≥ 1/14.
Construction of perfect strict optical orthogonal codes with weights 3 and 4.
Abstract
Perfect difference families (PDFs for short) are important both in theoretical and in applications. Perfect difference matrices (PDMs for short) and the equivalent structure had been extensively studied and used to construct perfect difference families, radar array and related codes. The necessary condition for the existence of a PDM is and . So far, PDMs exist for odd with two definite exceptions of . In this paper, new recursive constructions on PDMs are investigated, and it is proved that there exist PDMs for any odd with two definite exceptions of and possible exceptions. A complete result of -PDFs with the ratio of block size no less than is obtained. As an application, a complete class of perfect strict optical orthogonal codes with…
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography
