We study the distinguishability of linearized Reed-Solomon (LRS) codes by defining and analyzing analogs of the square-code and the Overbeck distinguisher for classical Reed-Solomon and Gabidulin codes, respectively. Our main results show that the square-code distinguisher works for generalized linearized Reed-Solomon (GLRS) codes defined with the trivial automorphism, whereas the Overbeck-type distinguisher can handle LRS codes in the general setting. We further show how to recover defining code parameters from any generator matrix of such codes in the zero-derivation case. For other choices of automorphisms and derivations simulations indicate that these distinguishers and recovery algorithms do not work. The corresponding LRS and GLRS codes might hence be of interest for code-based cryptography.

翻译：我们通过分别定义并分析经典Reed-Solomon码和Gabidulin码中平方码区分器与Overbeck型区分器的模拟对象，研究了线性化Reed-Solomon（LRS）码的可区分性。主要结果表明：对于由平凡自同构定义的广义线性化Reed-Solomon（GLRS）码，平方码区分器有效；而Overbeck型区分器能够在一般环境下处理LRS码。我们进一步展示了在零导子情况下，如何从这类码的任意生成矩阵中恢复其定义码参数。对于其他自同构与导子的选择，仿真实验表明这些区分器与恢复算法均不适用。因此，相应的LRS码和GLRS码可能对基于编码的密码学具有潜在价值。