A New Construction of Non-Binary Deletion Correcting Codes and their Decoding

TL;DR

This paper introduces a novel explicit construction of non-binary multiplicity-free deletion-correcting codes, demonstrating their ability to correct multiple deletions with larger sizes than previous codes and providing an effective decoding algorithm.

Contribution

The paper presents a new explicit construction of non-binary multiplicity-free codes based on set and permutation codes, capable of correcting multiple deletions.

Findings

Codes can correct multiple deletions.

Constructed codes have larger size than previous codes in certain regimes.

Decoding algorithm effectively recovers original codewords.

Abstract

Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new explicit construction of such codes, based on set and permutation codes. We show that our multiplicity-free codes can correct multiple deletions and provide a decoding algorithm. We also show that, for a certain regime of parameters, our constructed codes have size larger than all the previously known non-binary codes correcting multiple deletions.