We construct a new family of permutationally invariant codes that correct $t$ Pauli errors for any $t\ge 1$. We also show that codes in the new family correct spontaneous decay errors as well as deletion errors. In many cases the codes in this family are shorter than the best previously known explicit families of permutationally invariant codes both for Pauli errors, deletions, and for the amplitude damping channel. As a separate result, we generalize the conditions for permutationally invariant codes to correct $t$ Pauli errors from the previously known results for $t=1$ to any number of errors. For small $t$, these conditions can be used to construct new examples of codes by computer.

翻译：我们构造了一个新的置换不变码家族，该家族能够针对任意 $t\ge 1$ 的情况纠正 $t$ 个泡利错误。同时证明，新家族中的码还能纠正自发衰减错误及删除错误。在许多情况下，无论是用于纠正泡利错误、删除错误还是振幅阻尼信道，该家族中的码长度均优于此前已知最优的显式置换不变码家族。作为独立成果，我们将置换不变码纠正 $t$ 个泡利错误的条件从先前已知的 $t=1$ 情形推广至任意错误数。对于较小的 $t$ 值，这些条件可用于通过计算机构造新的码实例。