Modified Uniformly Redundant Array
A modified uniformly redundant array (MURA) is a type of mask used in coded aperture imaging. They were first proposed by Gottesman and Fenimore in 1989. Mathematical Construction of MURAs. MURAs can be generated in any length "L" that is prime and of the form the first five such values being formula_2. The binary sequence of a linear MURA is given by formula_3, where These linear MURA arrays can also be arranged to form hexagonal MURA arrays. One may note that if formula_5 and formula_6, a uniformly redundant array(URA) is a generated. As with any mask  in coded aperture imaging, an inverse sequence must also be constructed. In the MURA case, this inverse "G" can be constructed easily given the original coding pattern "A": Rectangular MURA arrays are constructed in a slightly different manner, letting formula_8, where and The corresponding decoding function "G" is constructed as follows: