Almost Hadamard circulants construction methods and their possible applications

Some new construction methods of almost Hadamard circulants (AHC) are proposed (pure ones does'nt exist if $N>4$). AHC deliver practically optimal solution for finding of most stable inverse operator in coded aperture method for needs of the emission tomography. Also they may be applied in coding theory for finding most noisestable codes. AHC have advantages comparing incidences matrices of ($\nu,k,\lambda$)-configurations usually applied for these aims because AHC exist for all $N$, have the more stable inverse operator and less complexity of construction $O(N\ln N)$.