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:本文在代数数域扩展中提出构造无限序列的有限非线性局部可恢复码 $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ 的方法。我们所构造的码有不断增长的长度和大小,恒定比特率、固定局部性,并最小距离趋近于无穷。