Abstract
Context. The problem of constructing a set of barcode patterns for multicolor barcodes that are resistant to distortions of one or two elements within each pattern is considered.
 Objective. The goal of the work is ensuring the reliability of the reading of multi-color barcode images.
 Method. A multicolor barcode pattern has the property of interference immunity if its digital equivalent (vector) is a codeword of a multi-valued (non-binary) correcting code capable to correct errors (distortions of the pattern elements). It is shown that the construction of barcode patterns should be performed on the basis of a multi-valued correcting BCH code capable to correct two errors. A method is proposed for constructing a set of interference-resistant barcode patterns of a given capacity, which ensure reliable reproduction of data when they are read from a carrier. A procedure for encoding data with a multi-valued BCH code based on the generator matrix of the code using operations by the modulo of a prime number has been developed. A new method of constructing the check matrix of the multivalued BCH code based on the vector representation of the elements of the finite field is proposed. A generalized algorithm for generating symbologies of a multi-color barcode with the possibility of correcting double errors in barcode patterns has been developed. The method also makes it possible to build symbology of a given capacity based on shortened BCH codes. A method of reducing the generator and check matrices of a multi-valued full BCH code to obtain a shortened code of a given length is proposed. It is shown that, in addition to correction double errors, multi-valued BCH codes also make it possible to detect errors of higher multiplicity – this property is enhanced when using shortened BCH codes. The method provides for the construction of a family of multicolor noise-immune barcodes.
 Results. On the basis of the developed software tools, statistical data were obtained that characterize the ability of multi-valued BCH codes to detect and correct errors, and on their basis to design multi-color interference-resistant bar codes.
 Conclusions. The conducted experiments have confirmed the operability of the proposed algorithmic tools and allow to recommend it for use in practice for developing interference-resistant multi-color barcodes in automatic identification systems.
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