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

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

2009-09-14

arxiv.org/abs/0909.2526v2

Computer Science

Information Theory

v2: a correction concerning shortened codes of length 12

Scientific paper

10.1007/s10623-010-9450-4

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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