Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known results and bounds for codes over fields. In particular, we propose a new family of locally recoverable codes by extending a construction proposed in 2014 by Tamo and Barg, and we discuss its optimality.

翻译：局部可恢复码处理的任务是依赖比信息集更小的剩余坐标子集来重建丢失的符号。我们考虑有限链环上码的情形，推广了域上码的已知结果与界。特别地，通过扩展Tamo和Barg于2014年提出的构造，我们提出了一类新的局部可恢复码族，并讨论了其最优性。