Barcode ISO standards can be confusing, here is a high-level summary of each standard to help you figure out which ISO standard is right for your barcoding applications.
15416 covers regular 1D barcodes, such as UPC. It is the document that specified how to grade these and defines the parameters such as Decodability, Symbol Contrast, etc.
15415 covers 2D barcodes, such as Data Matrix. It defines parameters such as Axial Non-uniformity and Fixed Pattern Damage. This document also covers stacked multi-row symbols such as PDF 417 which have something in common with 1D barcodes, but that is not what is usually referred to when discussing 15415.
15426 has two parts, -1 (as in “15426 dash 1”) AND -2.
15426-1 covers conformance (accuracy) to 15416 for verifiers and it defines the test symbols that are used to demonstrate conformance such as the symbols on the calibration card that contain tests for Decodability, Defect and the other parameters.
15426-2 covers conformance to 15415 and defines test symbols that are used to demonstrate that a verifier accurately measures the parameters defined in 15415.
There are a few other documents worth mentioning:
16022 – This is the symbology specification for Data Matrix and contains specific quality tests for Data Matrix symbols that cover the Fixed pattern of Data Matrix such as the “L sides”, clock tracks, and quiet zones. There are likewise documents for each other symbology that define specific symbology specific parameters for each symbology.
29158 – This is the “Direct Part Marking” grading document that gives a modification to 15415 for applying to symbols that are sometimes etched into metal or other materials and typically are read with different types of scanners, and so this grading method has been “tweaked” to measure the “readability” of such symbols in a way that is closer to the methods used by those types of scanners.