Apparatus and methods for calculating constant amplitude zero auto-correlation sequences are disclosed. One method includes calculating an argument of trigonometric functions used for calculating a constant amplitude zero auto-correlation sequence based at least on additive recursion of an input sequence root constant and without multiplication by a variable. A constant amplitude zero auto-correlation sequence is then computed using a CORDIC algorithm configured to calculate trigonometric functions used in determining the sequence without performing multiplication operations and based on the calculated argument. The disclosed methods and apparatus may be applied, in particular, to efficiently computing Zadoff-Chu sequences in preamble detection in particular physical random access channels in Long Term Evolution LTE communication systems. By allowing computation of such sequences, memory requirements can be reduced.