An n-node network, with its nodes numbered from - ën/2û to én/2ù - 1, is a chordal ring with chord lengths 1=s0<s1<...<sk-1<n/2 when an arbitrary node j - ën/2û £ j< én/2ù) is connected to each of the 2k nodes j ± t ai mod n (0£ i<k) via an undirected link, where "mod" represents (nearly) symmetric residues in [- ën/2û, én/2ù - 1].We study a class of chordal rings in which the chord length si is a power of an odd "radix" r, that is, si=ri, for r=2a+1 ³ 3. We show that this class of chordal rings, with their nodes indexed by radix-r integers using the symmetric digit set [-a, a], are easy to analyze and offer a number of advantages in tenns of static network parameters and dynamic performance for many application contexts. In particular, these networks allow a very simple optimal (shortest-path) routing algorithm that generates balanced traffic. We then briefly discuss fault tolerance properties of our networks and point out a number of variations and extensions to the basic structure.