The symmetry of HK codes representing close-packed structures and the efficient generation of non-equivalent polytypes of a given length

The HK representation of close-packed polytypes is studied as a binary code. It is shown that the HK code can be seen as operators forming a group. The neutrality condition is then translated to HK sequences that result in the identity operator. The symmetry of an HK word can be related to the space-group symmetry of the corresponding polytype. All HK code types corresponding to all possible close-packed space groups are reported. From a coding perspective, equivalent HK codes correspond to bracelet equivalent classes. An efficient algorithm with execution time constant per generated object is modified to generate all non-equivalent polytypes of a given length.