This paper addresses turbo codes with component convolutional codes as those in the Long Term Evolution (LTE) standard. We consider the interleaver lengths of the form $L=32k_L\Psi$, with $k_L\in \{1,3\}$ and $\Psi$ is a product of prime numbers greater than three. For these interleaver lengths, we have shown that a true cubic permutation polynomial (CPP) $f_{1}x+f_2{x}^2+f_3{x}^3\left(\mathrm{mod}L\right)$, under the constraint $f_3=0\left(\mathrm{mod}{p}_i\right)$ when a prime $p_i>3$ and 3 does not divide $(p_i-1)$, always has an inverse true CPP, except when $f_3=L∕\left(4k_L\right)$ and $f_2\in \{L∕16,3L∕16,5L∕16,7L∕16\}$. For the previously mentioned exception, a true CPP has an inverse true quadratic PP (QPP). For CPP interleavers with true inverse CPPs, we have shown that the minimum distance is upper bounded by the values of 44, 36, and 27, for three different classes of coefficients. Previously, it was shown that for the same interleaver lengths and for QPP interleavers, the upper bound on the minimum distance is equal to 50. Due to the symmetry of the classical turbo codes, the minimum distance is also upper bounded by the value of 50 for CPP interleavers with a QPP inverse. The nonlinearity degrees for all considered CPP interleavers are computed. Several examples of $d_{min}$-optimal CPP interleavers and their inverse QPPs are given.

与长期演进（LTE）标准中的内容一样，本文介绍了带有分量卷积码的Turbo码。我们考虑形式的交织器长度$\mathrm{大号}=32{ķ}_{\mathrm{大号}}\Psi$，带有 ${ķ}_{\mathrm{大号}}\in \{\mathrm{1个}，3\}$ 和 $\Psi$是质数大于3的乘积。对于这些交织器长度，我们已经证明了真正的三次置换多项式（CPP）$F_{\mathrm{1个}}X+F_2{X}^2+F_3{X}^3（\mathrm{模}\mathrm{大号}）$，在约束下 $F_3=0（\mathrm{模}{p}_{\mathrm{一世}}）$ 当素数 $p_{\mathrm{一世}}>3$ 和3不除 $（p_{\mathrm{一世}}-\mathrm{1个}）$，除非条件为 $F_3=\mathrm{大号}∕（4{ķ}_{\mathrm{大号}}）$ 和 $F_2\in \{\mathrm{大号}∕16，3\mathrm{大号}∕16，5\mathrm{大号}∕16，7\mathrm{大号}∕16\}$。对于前面提到的例外，真实CPP具有反向真实二次PP（QPP）。对于具有真正逆CPP的CPP交织器，我们已经表明，对于三种不同类别的系数，最小距离由44、36和27的值上限。以前，已证明对于相同的交织器长度和QPP交织器，最小距离的上限等于50。由于经典Turbo码的对称性，最小距离也由50的值上限CPP交错与QPP逆。计算所有考虑的CPP交织器的非线性度。几个例子$d_{米\mathrm{一世}ñ}$给出了最佳CPP交织器及其反向QPP。