Background. Nowadays, matrix barcodes in general and QR codes in particular are widely used in multiple applications, when it is important to input data into a computer system in a fast and secure way (both error-free and protected from third parties). Their popularity was significantly increased since the era of smartphones had begun, and so consequently, new use cases and new problems have arisen. Specifically, one of the important issues is representing more information as a barcode symbol. Objective. The objective of the research is to develop a data barcoding method based on grayscale tricolor 2D barcode which enables representing more amounts of information with preservation of the area of a graphical symbol. Methods. The research is based on both the coding theory and the multicolor barcode concept, which allow to increase amounts of data that can be encoded and represented by one matrix barcode symbol. The proposed BGW barcoding method uses a combination of data transformations between several notation systems with the purpose of data compression.Results. The method of data encoding based on tricolor matrix barcodes is proposed and described. This method allows to compress input alphanumeric data and transform it into a 2D barcode symbol composed of BGW (black, gray, white) barcode patterns. Two use cases for the proposed method application are considered in the paper. The first use case concerns enhanced information input. The second one addresses the data protection issue. Conclusions. The proposed BGW barcoding method enables compact representation of a textual data. One of the benefits of the proposed method lies in a possibility to not only encode data but to compress it. Due to data compression, more information can be represented keeping the same dimensions of the graphically coded symbol. Depending on the parameters, especially barcode symbol digital capacity, compression can be up to 20-25%.

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.