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

A new family of universal codes for binary data is introduced, based on recursion over computable characteristics of the content (popcount, pairwise XOR) rather than the length of the representation. Impossible states — bit patterns that cannot arise in valid encodings — are identified as free coding space. Delimiters in Elias gamma and omega are shown to be implicit instances of this principle. Classical codes (gamma, delta, omega, VByte, LEB128) are unified as 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.20139013
Primary Topic
Cellular Automata and Applications
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)
Cellular Automata and Applications
preprint

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

Max Permyakov
preprint en

Abstract

A new family of universal codes for binary data is introduced, based on recursion over computable characteristics of the content (popcount, pairwise XOR) rather than the length of the representation. Impossible states — bit patterns that cannot arise in valid encodings — are identified as free coding space. Delimiters in Elias gamma and omega are shown to be implicit instances of this principle. Classical codes (gamma, delta, omega, VByte, LEB128) are unified as instances of a single parameterized construction.

Zenodo (CERN European Organization for Nuclear Research)
Cellular Automata and Applications
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