4-*GDD(6n)s and Related Optimal Quaternary Constant-Weight Codes

Authors


  • Contract grant sponsor: National Outstanding Youth Science Foundation of China, contract grant number: 10825103; contract grant sponsor: National Natural Science Foundation of China, contract grant number: 61171198; contract grant sponsor: Specialized Research Fund for the Doctoral Program of Higher Education, and Zhejiang Provincial Natural Science Foundation of China, contract grant number: D7080064.

Abstract

Constant-weight codes (CWCs) have played an important role in coding theory. To construct CWCs, a K-GDD (where GDD is group divisible design) with the “star” property, denoted by K-*GDD, was introduced, in which any two intersecting blocks intersect in at most two common groups. In this paper, we consider the existence of 4-*GDDmath formulas. Previously, the necessary conditions for existence were shown to be sufficient for math formula, and also sufficient for math formula with prime powers math formula and math formula. We continue to investigate the existence of 4-*GDD(6n)s and show that the necessary condition for the existence of a 4-*GDD(6n), namely, math formula, is also sufficient. The known results on the existence of optimal quaternary (n, 5, 4) CWCs are also extended.

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