On the nonperiodic cyclic equivalence classes of Reed-Solomon codes

Picking up exactly one member from each of the nonperiodic cyclic equivalence classes of an (n, k+1) Reed-Solomon code E over GF(q) gives a code, E", which has bounded Hamming correlation values and the self-synchronizing property. The exact size of E" is shown to be (1/n) Sigma /sub d mod n/ mu (d)q/sup 1+k/d/, where mu (d) is the Mobius function, (x) is the integer part of x, and the summation is over all the divisors d of n=q-1. A construction for a subset V of E is given to prove that mod E" mod >or= mod V mod =(q/sup k+1/-q/sup k+1-N/)/(q-1) where N is the number of integers from 1 to k which are relatively prime to q-1. A necessary and sufficient condition for mod E" mod = mod V mod is proved and some special cases are presented with examples. For all possible values of q>2, a number B(q) is determined such that mod E" mod = mod V mod for 1 mod V mod for k>B(q). >