Mathematics of CRC
Mathematical analysis of this division-like process reveals how to select a divisor that guarantees good error-detection properties. In this analysis, the digits of the bit strings are thought of as the coefficients of a polynomial in some variable x—coefficients that are elements of the finite field GF(2), instead of more familiar numbers. This binary polynomial is treated as a ring. A ring is, informally, a set of elements somewhat like numbers, with an operation resembling addition and an operation resembling multiplication. These operations possess many of the familiar arithmetic properties of commutativity, associativity, and distributivity. Ring theory is part of abstract algebra.
Read more about this topic: Cyclic Redundancy Check
Famous quotes containing the word mathematics:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)