Two optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes
The optimal one-error-correcting codes of length 13 that are doubly shortened perfect codes are classified utilizing the results of [A-stergAyenrd, P.R.J., Pottonen, O.: The perfect binary one-error-correcting codes of length 15: Part I-Classification. IEEE Trans. Inform. Theory 55, 4657-4660 (2009)]; there are 117821 such (13,512,3) codes. By applying a switching operation to those codes, two more (13,512,3) codes are obtained, which are then not doubly shortened perfect codes.
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