New 2-designs from strong difference families

2017/02/24 by Simone Costa, Tao Feng, Costa, Simone +3
Computer Science · Engineering · Medicine · #Cancer Mechanisms and Therapy #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1702.07500

openalex publication_date 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to 2-designs, and have applications in constructions for many significant codes, such as optical orthogonal codes and optical orthogonal signature pattern codes. In this paper, with a careful use of cyclotomic conditions attached to strong difference families, we improve the lower bound on the asymptotic existence results of (\mathbbF_p× \mathbbF_q,\mathbbF_p× \0\,k,λ)-DFs for k∈\p,p+1\. We improve Buratti's existence results for 2-(13q,13,λ) designs and 2-(17q,17,λ) designs, and establish the existence of seven new 2-(v,k,λ) designs for (v,k,λ)∈\(694,7,2),(1576,8,1),(2025,9,1),(765,9,2),(1845,9,2),(459,9,4), (783,9,4)\.

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