Embedding in a perfect code

Abstract

A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length

Eng: 5pp, Rus: 5pp. V3: revised, a survey added; the accepted version; Russian translation added

References in corpus (1)

• On the number of 1-perfect binary codes: a lower bound

Cited by in corpus (5)

• The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
• The extended 1-perfect trades in small hypercubes
• Two Optimal One-Error-Correcting Codes of Length 13 That Are Not Doubly Shortened Perfect Codes
• Embedding in $q$-ary $1$-perfect codes and partitions
• Full-Rank Perfect Codes over Finite Fields