Constructions of augmented orthogonal arrays. Issue 11 (1st September 2018)

• Record Type: Journal Article
• Authors: Wang, Xin; Ji, Lijun; Li, Yun; Liang, Miao
• Is Part Of: Journal of combinatorial designs. Volume 26:Issue 11(2018:Nov.)
• Page Start: 547
• Page End: 559
• Publication Date: 2018-09-01
• Subjects: augmented orthogonal array -- ideal ramp scheme -- orthogonal array; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21624
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: Augmented orthogonal arrays (AOAs) were introduced by Stinson, who showed the equivalence between ideal ramp schemes and AOAs (Discrete Math. 341 (2018), 299–307). In this paper, we show that there is an AOA ( s, t, k, v ) if and only if there is an OA ( t, k, v ) which can be partitioned into v t − s subarrays, each being an OA ( s, k, v ), and that there is a linear AOA ( s, t, k, q ) if and only if there is a linear maximum distance separable (MDS) code of length k and dimension t over F q, which contains a linear MDS subcode of length k and dimension s over F q . Some constructions for AOAs and some new infinite classes of AOAs are also given.