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arXiv · 0909.2526

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

Patric R. J. Östergård·Olli Pottonen
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Abstract

The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. \"Osterg{\aa}rd 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.

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Patric R. J. Östergård, Olli Pottonen. 2009-09-14. Two Optimal One-Error-Correcting Codes of Length 13 That Are Not Doubly Shortened Perfect Codes. https://doi.org/10.1007/s10623-010-9450-4

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