In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic number fields. The codes in our sequences have increasing length and size, constant rate, fixed locality, and minimum distance going to infinity.

翻译：本文给出了无限序列的有限非线性局部可恢复码 $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ 的构造方案，这些码定义在有限域的乘积之上，源于代数数域中的基展开。我们所得序列中的码具有递增的长度和规模、恒定的码率、固定的局部性，且最小距离趋于无穷大。