System for determining positions (P, Px, Py, Pz) along a direction of advance (F, Fx, Fy, Fz), comprising: • a first sensor with an array of detectors having a scanning length along a longitudinal axis, which first sensor is used for scanning a first pattern (5, 5') and producing a scan signal and is integrated in a first scanning head, • a first 2D pattern (5, 5') that can be scanned by the first sensor, extending in the direction of advance (F, Fx, Fy, Fz) and comprising pattern elements (6, 6a-6f), wherein the first sensor and the first 2D pattern (5, 5') are mobile relative to one another in the direction of advance (F, Fx, Fy, Fz), and • a control and evaluation unit for evaluating the scan signal, wherein • the pattern elements (6, 6a-6f) form an associated first code word for each position (P, Px, Py, Pz) along the direction of advance (F, Fx, Fy, Fz) by virtue of arrangement and/or embodiment that is/are different by definition, which first code word can be sensed in each case at least on a portion of the scanning length of the first sensor and which first code word codes the respective position absolutely, so that the first 2D pattern (5, 5') forms an absolute position code trace in the direction of advance (F, Fx, Fy, Fz), and • the scan signal in the respective position (P, Px, Py, Pz) corresponds to the first code word in each case, characterized in that the following information is stored in the control and evaluation unit: □ a piece of decoding information that can be used to uniquely associate an absolute position with each scan signal, and □ information that can be used to determine, on the basis of the first code word, in the respective position (P, Px, Py, Pz), using the respective scan signal, a deviation of the first sensor from an ideal position (9, 10, 12) relative to the first 2D pattern (5, 5') at least in respect of one degree of freedom of movement. • a first sensor with an array of detectors having a scanning length along a longitudinal axis, which first sensor is used for scanning a first pattern (5, 5') and producing a scan signal and is integrated in a first scanning head, • a first 2D pattern (5, 5') that can be scanned by the first sensor, extending in the direction of advance (F, Fx, Fy, Fz) and comprising pattern elements (6, 6a-6f), wherein the first sensor and the first 2D pattern (5, 5') are mobile relative to one another in the direction of advance (F, Fx, Fy, Fz), and • a control and evaluation unit for evaluating the scan signal, wherein • the pattern elements (6, 6a-6f) form an associated first code word for each position (P, Px, Py, Pz) along the direction of advance (F, Fx, Fy, Fz) by virtue of arrangement and/or embodiment that is/are different by definition, which first code word can be sensed in each case at least on a portion of the scanning length of the first sensor and which first code word codes the respective position absolutely, so that the first 2D pattern (5, 5') forms an absolute position code trace in the direction of advance (F, Fx, Fy, Fz), and • the scan signal in the respective position (P, Px, Py, Pz) corresponds to the first code word in each case, □ a piece of decoding information that can be used to uniquely associate an absolute position with each scan signal, and □ information that can be used to determine, on the basis of the first code word, in the respective position (P, Px, Py, Pz), using the respective scan signal, a deviation of the first sensor from an ideal position (9, 10, 12) relative to the first 2D pattern (5, 5') at least in respect of one degree of freedom of movement.