Move the sampling window. The message changes.

Two equal-size QR matrices occupy the same image. A small centered region in every module carries the near code; the surrounding region carries the far code.

PAPER-STYLE CONSTRUCTION / STANDARD QR READERS / PHYSICAL RESULTS VARY

DUAL-MESSAGE LAB

One image, two sampling apertures

The defaults reproduce the paper's first example parameters: version 1, ECC L, 29-pixel modules, and a 7-pixel centered near region.

Predict first

The same image, resampled through a narrower aperture. What does it decode to?

The same message A different message

Sampling aperture 7 x 7 px / near

DUAL QR

SAMPLED MATRIX

WHAT THE SCANNER SEES / FAR

—

WHAT CHANGED UNDERNEATH

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WHAT A SECOND READER CAN RECOVER / NEAR

—

HOW AN ANALYST CAN NOTICE

Modules are not solid. Each one holds a centered region that can differ from its surround, so magnification — or a second decode at a different sampling aperture — exposes the construction.

CURRENT SAMPLED DECODE

—

near 0 / far 0

near 0 / far 1

near 1 / far 0

near 1 / far 1

IMPLEMENTATION SCOPE

The module-value decision is itself a representational layer.

This implementation follows Chou and Wang's generating algorithm: both messages use standard QR codes with the same version and ECC level; each corresponding bit pair selects one of four two-state module blocks; the centered region carries the near value and the outer region carries the far value; a four-module quiet zone surrounds the result.

The browser proves both matrices by resampling the rendered composite and decoding them with ZXing. Physical phone results still depend on screen density, camera focus, app behavior, glare, and distance. The paper reports near/far reads at about 30/50 cm on a monitor and 20/40 cm on paper for one setup, not universal thresholds.

Implemented from: Kuo-Cheng Chou & Ran-Zan Wang, “Dual-Message QR Codes,” Sensors 24(10):3055 (2024). doi:10.3390/s24103055 FULL

Read the research note