We consider a generalized concatenated construction for error-correcting codes over the q-ary alphabet in the modulus metric L₁ and Lee metric L. Resulting codes have arbitrary length, arbitrary distance (independently of the alphabet size), and can correct both independent errors and error bursts in both metrics. In particular, for any length 2^m we construct codes over \(\mathbb{Z}_4\) with Lee distance 4 which under the Gray mapping yield extended binary perfect codes of length 2^m+1 (with code distance 4). We construct codes over \(\mathbb{Z}_4\) of length n with Lee distance n which under the Gray mapping yield Hadamard matrices of order 2n (under the additional condition that an Hadamard matrix of order n exists). The constructed new codes in the Lee metric are often better in their parameters than previously known ones; in particular, they are essentially better than previously constructed Astola codes.

我们考虑模量度量L ₁和Lee度量L中的q元字母表上的纠错码的广义级联构造。所得代码具有任意长度，任意距离（与字母大小无关），并且可以在两个度量标准中校正独立错误和错误突发。特别是，对于任何长度2 ^m，我们在Lee距离4的\（\ mathbb {Z} _4 \）上构造代码，在格雷映射下，该代码会生成长度为2 ^{m +1的}扩展二进制完美代码（代码距离为4）。我们构造长度为n的\（\ mathbb {Z} _4 \）且李距离为n的代码在灰色映射下得出2 n阶的Hadamard矩阵（在附加条件下，存在n阶的Hadamard矩阵）。Lee度量标准中构造的新代码的参数通常比以前已知的更好。特别是，它们本质上比以前构造的Astola码更好。