Abstract
Motivated by the information transmission in neurons with various applications in in-vivo nano-machines or emerging medical applications, Ye and Elishco [2023] introduced a communication channel, called the absorption channel, and proposed codes correcting absorption errors. For a non-binary alphabet \Sigma_{q} , the authors presented constructions of codes of length n correcting a single absorption and the best construction yielded a redundancy of \log_{q}n+12\log_{q}\log_{q}n+O(1) symbols. In this work, we make progress on the code design problem above and show that the redundancy can be further reduced significantly as follows: When q=3 , we construct "nearly optimal" ternary codes of length n with at most \log_{3}n+5.43 redundant symbols. Note that such a redundancy is optimal up to a constant. * For a general alphabet \Sigma_{q} , we construct q-ary codes of length n correcting a single absorption error with \log_{q}n+3\log_{q}\log_{q}n+O(1) redundant symbols, providing an alternative. simpler construction that improves the results given by Ye and Elishco.