We consider the problem of efficient construction of q-ary 2-deletion correcting codes with low redundancy. We show that our construction requires less redundancy than any existing efficiently encodable q-ary 2-deletion correcting codes. Precisely speaking, we present an explicit construction of a q-ary 2-deletion correcting code with redundancy 5 log(n)+10log(log(n)) + 3 log(q)+O(1). Using a minor modification to the original construction, we obtain an efficiently encodable q-ary 2-deletion code that is efficiently list-decodable. Similarly, we show that our construction of list-decodable code requires a smaller redundancy compared to any existing list-decodable codes. To obtain our sketches, we transform a q-ary codeword to a binary string which can then be used as an input to the underlying base binary sketch. This is then complemented with additional q-ary sketches that the original q-ary codeword is required to satisfy. In other words, we build our codes via a binary 2-deletion code as a black-box. Finally we utilize the binary 2-deletion code proposed by Guruswami and Hastad to our construction to obtain the main result of this paper.

翻译：我们研究高效构造低冗余的q元2-删除纠正码问题。结果表明，我们的构造相比现有所有可高效编码的q元2-删除纠正码具有更低的冗余。具体而言，我们给出了一种q元2-删除纠正码的显式构造，其冗余为5 log(n)+10log(log(n)) + 3 log(q)+O(1)。通过对原始构造进行轻微修改，我们获得了一种可高效列表解码的q元2-删除码。类似地，我们证明所构造的列表解码码相比现有列表解码码具有更小的冗余。为实现所需的草图，我们将q元码字转换为二进制字符串，该字符串可作为底层基础二进制草图的输入，并辅以原始q元码字需满足的额外q元草图。换言之，我们以二进制2-删除码为黑盒构建了码字。最后，我们采用Guruswami和Hastad提出的二进制2-删除码应用于我们的构造，从而得到本文的主要结果。