The present disclosure provides methods of generating supports (e.g., beads) comprising barcode molecules coupled thereto. A barcode molecule coupled to a support may comprise a barcode sequence and a functional sequence. A barcode molecule may be generated using two or more ligation reactions in a combinatorial fashion. A support comprising two or more different barcode molecules may be useful for analyzing or processing one or more analytes such as nucleic acid molecules, proteins, and/or perturbation agents.

A single dual-sided product placement and information strip includes a first side with product information for consumers and a second side with product placement information for placing products on a display shelf. The dual-sided product placement and information strip enables information necessary for consumers to be printed on the first (consumer-facing) side and information that assists stockers to place products on shelves to be printed on the second (opposing) side. Also disclosed are systems and methods for formatting and printing the dual-sided product placement and information strips. The single dual-sided product placement and information strip may be printed alone or in a single sheet along with one or more other dual-sided product placement and information strips.

A method for providing information in a machine-readable form is based on information being allocated a unique database reference identifier consisting of at least one character in an initialization step. In a subsequent generation process step, a 2D identifier matrix is generated. The 2D identifier matrix has cells, each of which is assigned a cell value. The 2D identifier matrix has linear borders for bordering the cells. The borders and the cells are designed such that the cell values can be optically detected by a person. Immediately following the generation of the 2D identifier matrix, the database reference identifier is transmitted to the 2D identifier matrix by marking specified cells of the 2D identifier matrix in the same generation process step. Each character of the database reference identifier is represented by precisely one cell value.

A system and method for use in authenticating one or both of a container and a product packaged therein. The method comprises obtaining images of each of two codes carried by a container system comprising the container. The method further comprises determining, for each image, a contrast ratio between one or more elements of the code in the image and the background of the code. The method still further comprises determining the authenticity of one or both of the container and the product packaged therein based at least in part on the contrast ratios for each image, and therefore, each code.

Container for a beverage or foodstuff preparation machine, the container for containing beverage or foodstuff material and comprising a code encoding preparation information, the code comprising a reference portion (80) and a data portion (78). The reference portion (80) comprises three reference units (86) defining a reference line (81), the three reference units (86) being arranged at the vertices of an isosceles reference triangle having a reference apex angle. The data portion comprises discrete positions (75) at locations determined relative to the reference line (81), each discrete position either comprises or does not comprise a data unit (82) to at least partially encode the preparation information, wherein the discrete positions (75) are arranged at vertices of a grid of isomorphic tessellating isosceles data triangles, the data triangles having a data apex angle different from the reference apex angle.

A server is used to receive a barcode generation request sent by an end-user device. The server is used to generate, based on the barcode generation request, at least two pieces of barcode information by using at least two code systems, respectively. The server is used to transmit a barcode generation response to the end-user device, where the barcode generation response includes the at least two pieces of barcode information, where the barcode generation response causes an application running on the end-user device to display on the end-user device, alternately, a respective barcode image corresponding to each piece of the at least two pieces of barcode information.

A system and method for use in authenticating one or both of a container and a product packaged therein. The method comprises obtaining images of each of two codes carried by a container system comprising the container. The method further comprises determining, for each image, a contrast ratio between one or more elements of the code in the image and the background of the code. The method still further comprises determining the authenticity of one or both of the container and the product packaged therein based at least n part on the contrast ratios for each image, and therefore, each code.

The present disclosure provides methods of generating supports (e.g., beads) comprising barcode molecules coupled thereto. A barcode molecule coupled to a support may comprise a barcode sequence and a functional sequence. A barcode molecule may be generated using two or more ligation reactions in a combinatorial fashion. A support comprising two or more different barcode molecules may be useful for analyzing or processing one or more analytes such as nucleic acid molecules, proteins, and/or perturbation agents.

At least some embodiments of the present invention relate to approaches for displaying encoded information and systems used to capture said information. In an embodiment, the present invention is a method that includes: providing a product packaging having a first face; providing a first symbology on the first face; providing a second symbology on the first face; and providing a third symbology on the first face, wherein the second symbology is the first symbology distorted in accordance with a first distortion function, the first distortion function distorting at least one of an aspect ratio and a skew pursuant to a first parameter; and wherein the third symbology is the first symbology distorted in accordance with a second distortion function, the second distortion function distorting at least one of the aspect ratio and the skew pursuant to a second parameter, the second parameter being different from the first parameter.

An optically readable tag and methods and systems for decoding the optically readable tag are disclosed. The optically readable tag comprises: a border region having an indicative shape; and an encoding region, defined by the border region, the encoding region comprising a plurality of encoding shape objects, wherein data is encoded by relative sizes of the encoding shape objects.