Two Optimal One-Error-Correcting Codes of Length 13 That Are Not Doubly Shortened Perfect Codes
Patric R. J. \"Osterg{\aa}rd, Olli Pottonen
TL;DR
This paper identifies two specific length-13 codes that are optimal one-error-correcting but are not derived from perfect codes, expanding understanding of code structures beyond known classifications.
Contribution
It introduces two new (13,512,3) codes obtained via switching, which are not doubly shortened perfect codes, challenging previous classifications.
Findings
117821 doubly shortened perfect codes classified
Two new codes obtained through switching operations
The new codes are not doubly shortened perfect codes
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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