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

作者：Demirkale Fatih^*; Donovan Diane; Khodkar Abdollah

来源：Journal of Combinatorial Designs, 2015, 23(5): 195-203.

DOI：10.1002/jcd.21394

• Latin squares
• nearly orthogonal Latin squares
• orthogonal Latin squares
• quasi-difference sets

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.

• 出版日期2015-5