Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the corresponding eigenspaces, we provide an improved spectral bound for quasi-cyclic codes. Numerical results verify that the improved bound outperforms the Jensen bound in almost all cases. Based on the improved bound, we propose a general construction of quasi-cyclic codes with excellent designed minimum distances. For the quasi-cyclic codes produced by this general construction, the improved spectral bound is always sharper than the Jensen bound.

翻译：谱界是估计准循环码最小距离的有力工具。谱界将循环码的定义集界推广至准循环码。基于准循环码的特征值及相应特征空间，我们提出了一个改进的准循环码谱界。数值结果表明，在几乎所有情况下，改进后的谱界均优于Jensen界。基于改进的谱界，我们提出了一种具有优异设计最小距离的准循环码通用构造方法。对于该通用构造生成的准循环码，改进的谱界始终比Jensen界更优。