A Family of Universal Codes via Content-Aware Recursion and Impossible States

I introduce a family of universal codes for binary data that recurse on computable characteristics of the content (popcount, pairwise XOR) rather than on the length of the representation. I identify impossible states — bit patterns that cannot arise in valid encodings — as free coding space, and show that delimiters in Elias gamma and omega are implicit instances of this principle. I observe that classical codes (gamma, delta, omega, VByte, LEB128) are instances of a single parameterized construction.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-12
DOI
https://doi.org/10.5281/zenodo.20138769
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

A Family of Universal Codes via Content-Aware Recursion and Impossible States

Max Permyakov
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

A Family of Universal Codes via Content-Aware Recursion and Impossible States

Max Permyakov
preprint en

Abstract

I introduce a family of universal codes for binary data that recurse on computable characteristics of the content (popcount, pairwise XOR) rather than on the length of the representation. I identify impossible states — bit patterns that cannot arise in valid encodings — as free coding space, and show that delimiters in Elias gamma and omega are implicit instances of this principle. I observe that classical codes (gamma, delta, omega, VByte, LEB128) are instances of a single parameterized construction.

Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
DOIOpen Access PDFOpenAlex
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A Family of Universal Codes via Content-Aware Recursion and Impossible States — Max Permyakov · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS