Two Optimal One-Error-Correcting Codes of Length 13 That Are Not Doubly Shortened Perfect Codes

Authors

Patric R. J. Östergård, Olli Pottonen

Categories

Abstract

The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. Östergård and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification, IEEE Trans. Inform. Theory, to appear]; 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.