We study skew-tolerant Gray codes, which are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over the known construction. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of complete $m$-ary skew-tolerant Gray codes for every base $m\geq 3$.

翻译：本文研究容偏格雷码，即相邻码字仅在相邻位置发生变化的格雷码。我们首次提出了渐近非零容偏格雷码的构造方法，相比已知构造实现了指数级改进。同时，我们为所提出的编码方案提供了线性时间的编码与解码算法。最后，我们将该定义推广至非二进制字母表，并为所有基数$m\geq 3$构造了完备的$m$元容偏格雷码。