The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification
Information Theory
2015-03-13 v3 math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.0806.2513,
title = {The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification},
author = {Patric R. J. Östergård and Olli Pottonen},
journal= {arXiv preprint arXiv:0806.2513},
year = {2015}
}
Comments
6 pages. v3: made the codes available in the source of this paper