Direct Constructions for General Families of Cyclic Mutually Nearly Orthogonal Latin Squares

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Demirkale F., DONOVAN D., KHODKAR A.

JOURNAL OF COMBINATORIAL DESIGNS, vol.23, no.5, pp.195-203, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 5
  • Publication Date: 2015
  • Doi Number: 10.1002/jcd.21394
  • Journal Name: JOURNAL OF COMBINATORIAL DESIGNS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.195-203
  • Yıldız Technical University Affiliated: Yes

Abstract

Two Latin squares L=[l(i,j)] and M=[m(i,j)], of even order n with entries {0,1,2,...,n-1}, are said to be nearly orthogonal if the superimposition of L on M yields an nxn array A=[(l(i,j),m(i,j))] in which each ordered pair (x,y), 0x,yn-1 and xy, occurs at least once and the ordered pair (x,x+n/2) occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders 48k+14, 48k+22, 48k+38, and 48k+46. The techniques employed are based on the principle of Methods of Differences and so we also establish infinite classes of quasi-difference sets for these orders.