Efficient encoding for the moment-syndrome construction

Develop an efficient encoder for the multidimensional moment-syndrome CPC construction, which has nearly optimal redundancy and an explicit synchronization decoder but currently lacks an efficient encoding procedure.

Background

The moment-syndrome construction selects arrays whose support weight is relatively prime to the side length and whose coordinate moments satisfy a prescribed syndrome. These constraints enable direct recovery of an unknown multidimensional cyclic translation and yield asymptotically optimal redundancy for prime side lengths.

Although the construction provides a direct decoder and strong redundancy guarantees, the paper does not provide an efficient encoder for producing arrays satisfying the required moment and weight constraints. Developing such an encoder is therefore identified as an unresolved algorithmic problem.