Capacity of an infinite family of networks related to the diamond network for fixed alphabet sizes

The paper delves into the capacity of a generalized diamond network under adversarial conditions, where an adversary can manipulate a single edge. It builds on previous work on specific networks and provides a comprehensive combinatorial treatment. The main result, Theorem 1, simplifies the design of optimal network codes by reducing it to a covering problem. The paper sets lower and upper bounds for the 1-shot capacity, making it a significant contribution to the understanding of network coding under adversarial conditions.