Two Optimal One-Error-Correcting Codes of Length 13 That 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. Östergård 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.

v2: a correction concerning shortened codes of length 12

References in corpus (3)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification
• The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
• Embedding in a perfect code

Cited by in corpus (7)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
• On the binary codes with parameters of doubly-shortened 1-perfect codes
• On the OA(1536,13,2,7) and related orthogonal arrays
• On Optimal Binary One-Error-Correcting Codes of Lengths $2^m-4$ and $2^m-3$
• On the binary codes with parameters of triply-shortened 1-perfect codes
• On multifold packings of radius-1 balls in Hamming graphs
• On $q$-ary shortened-$1$-perfect-like codes