multicolor bar codes, multi-valued Hemming code, automatic identification


Background. In recent years, there has been a steady trend towards the using of multi-colored barcodes. This increases the information density of the data compared to black and white barcodes. However, this complicates the processes of recognition and decoding of bar code images. Therefore, in order to reliably read multi-colored barcodes from an object, it is necessary to ensure noise immunity of bar code patterns – the minimum structural units of the bar code image.

Objective. The purpose of the paper is development of a method for the synthesis of symbolics of multi-colored bar codes, which have the property of noise immunity at the level of bar code patterns.

Methods. This goal is achieved through the using of multivalued incomplete Hemming codes as the basis for constructing bar code patterns. The numerical equivalent of the bar code pattern is a code word of the multi-valued Hemming code, in which the encoding-decoding operations are performed according to the rules of a finite field GF(p).

Results. A number of error-correcting multi-colored barcodes have been proposed, in which one-time distorted element (error) is corrected at the level of barcode pattern and a significant number of multiple distortions are detected. The error-correcting capability of multi-colored barcode patterns has been evaluated.

Conclusions. The proposed method of the synthesis of symbolics of multi-colored barcodes allows creating barcodes with improved error-correcting characteristics, which provides the appropriate level of reliability of the process of reading multi-colored barcodes in automatic identification systems.


H. Bagherinia and R. Manduchi, “A theory of color barcodes,” in 2011 IEEE Int. Conf. Computer Vision Workshops (ICCV Workshops), Barcelona, Spain, 2011, pp. 806–813. doi: 10.1109/ICCVW.2011.6130335

J. Barrus and G.J. Wolf, “Embedding barcode data in an auxiliary field of an image file,” U.S. Patent 7 150 399, Dec. 19, 2006.

O. Tutsuya, M. Kazuhiro, “Layered two-dimensional code, creation method thereof, and read method,” U.S. Patent Application 20090166418, 2006.

High capacity color barcodes (HCCB) [Online]. Available:

A. Grillo et al., “High capacity colored two dimensional codes,” in Proc. Int. Multiconf. Computer Science and Information Technology, 2010, Oct. 18-20, pp. 709–716.

D. Parikh and G. Jancke, “Localization and segmentation of a 2D high capacity color barcode,” in IEEE Workshop on Applications of Computer Vision, 2008, Jan. 7-9, pp. 1–6. doi: 10.1109/WACV.2008.4544033

F. Wang and R. Manduchi, “Color-constant information embedding,” in Proc. IEEE Workshop Color Reflectance Imaging Computer Vision, 2010.

E.G. Miller and K. Tieu, “Color eigenflows: Statistical modeling of joint color changes,” in Proc. Eighth IEEE Int. Conf. Computer Vision (ICCV 2001), Vancouver, Canada, 2001, pp. 607–614. doi: 10.1109/ICCV.2001.937574

P. Cattrone, “Two-dimensional color barcode and method of generating and decoding the same,” U.S. Patent 7 478 746, Jan. 20, 2009.

M. Querini et al., “2D color barcodes for mobile phones,” Int. J. Comp. Sci. Appl., vol. 8, no. 1, pp. 136–155, 2011.

W. Wesley Peterson and E. J. Weldon, Jr., Error-Correcting Codes, 2nd ed. MIT, 1972, 560 p.

R.E. Blahut, Theory and Practice of Error Control Codes. Reading, MA: Addison-Wesley, 1983, 500 p.

T. Kasami et al. Theory Coding. Mir, 1978, 576 p.