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

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.

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

References in corpus (2)

• Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
• On the number of 1-perfect binary codes: a lower bound

Cited by in corpus (10)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
• Reconstructing Extended Perfect Binary One-Error-Correcting Codes from Their Minimum Distance Graphs
• On the OA(1536,13,2,7) and related orthogonal arrays
• On Optimal Binary One-Error-Correcting Codes of Lengths $2^m-4$ and $2^m-3$
• Two Optimal One-Error-Correcting Codes of Length 13 That Are Not Doubly Shortened Perfect Codes
• An enumeration of 1-perfect ternary codes
• A partition of the hypercube into maximally nonparallel Hamming codes
• Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code
• The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes
• Capacity of an infinite family of networks related to the diamond network for fixed alphabet sizes