Zero-error codes for the noisy-typewriter channel

In this paper, we propose nontrivial codes that achieve a non-zero zero-error rate for several odd-letter noisy-typewriter channels. Some of these codes (specifically, those which are defined for a number of letters of the channel of the form 2
ⁿ
+ 1) achieve the best-known lower bound on the zero-error capacity. We build the codes using linear codes over rings, as we do not require the multiplicative inverse to build the codes.