Embedding in a perfect code
Sergey Avgustinovich (Sobolev Institute of Mathematics, Novosibirsk,, Russia), Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)
TL;DR
This paper demonstrates that any binary 1-error-correcting code can be embedded into a larger 1-perfect code, showing a universal embedding property for these codes.
Contribution
It establishes the theoretical possibility of embedding any binary 1-error-correcting code into a larger 1-perfect code.
Findings
Any binary 1-error-correcting code can be embedded in a 1-perfect code.
The embedding preserves error-correcting properties.
This result broadens understanding of code embedding possibilities.
Abstract
A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length
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