The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification

Details The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification

2008-06-16

arxiv.org/abs/0806.2513v3

IEEE Trans. Inform. Theory 55 (2009), 4657-4660

Computer Science

Information Theory

6 pages. v3: made the codes available in the source of this paper

Scientific paper

10.1109/TIT.2009.2027525

A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5983 such inequivalent perfect codes and 2165 extended perfect codes. Efficient generation of these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-error-correcting codes of length 14 and the (15, 1024, 4) codes are also classified; there are 38408 and 5983 such codes, respectively.

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