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 t Cdln p(d)~~~+[$], where p(d) is the Miibius function, [z] is the integer part of 5, and the summation is over all the divisors d of n = 4 1. A construction for a subset V of E is given to prove that IE”I 2 IV] = (@+I p--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 IE”I = II/( is proved and some special cases are presented with examples. Furthermore, for all possible values of 4 > 2, a number B(q) is determined such that (E”l = II/( for 1 5 k 5 B(q) and JE”I > IV/ for k > B(q).