On operations of spatial ordering and location code

摘要

Spatial ordering is the numeral sequence of points in the n-dimensional integer space In. Many computational applications are based on spatial ordering. Analysis on spatial ordering can be conducted in three areas: algebraic structures, algebraic operations, and performance metrics. This paper mainly focuses on operations. Although the addition and multiplication may involve the finite group concept, the rotation and mirroring can be described by a Boolean algebraic approach called the Boolean formulation method. An alternative method, the polynomial mapping method, is also discussed.