On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

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16 November 2021

journal article
research article
Published by Wiley in Journal of Combinatorial Designs

Vol. 30 (2) , 73-90
DOI:10.1002/jcd.21812

Abstract

We give a direct construction of a

(Z_{p} \times G, {0} \times G, 4, 1)

relative difference family for

G \in {Z_{6} \times Z_{6}, Z_{2} \times Z_{18}, Z_{6} \times Z_{18}, Z_{2} \times Z_{54}}

and every prime

p \equiv 3 (\mod 4)

with

p > 3

. These allow us to construct an optimal

(Z_{6 m} \times Z_{6 n}, 4, 1)

difference packing and an optimal

(Z_{2 m} \times Z_{18 n}, 4, 1)

difference packing for every pair of positive integers

(m, n)

. The corresponding optimal optical orthogonal signature pattern codes are also obtained.

Keywords

Funding Information

Xinyang Normal University (Nanhu Scholars Program for Young Scholars)
National Natural Science Foundation of China (11871363, 11901503)

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