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This paper focuses on Hagiwara codes, which are quantum deletion-correcting codes constructed by the quantum Reed-Solomon codes. Although Hagiwara codes can correct composite errors consisting of deletions and insertions, an efficient…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
We generalize Helberg's number-theoretic construction of multiple insertion-deletion correcting binary codes to non-binary alphabets and describe a linear decoding algorithm for correcting multiple deletions.
This paper constructs a non-binary code correcting a single $b$-burst of insertions or deletions with a large cardinality. This paper also proposes a decoding algorithm of this code and evaluates a lower bound of the cardinality of this…
We present the first known efficient decoding algorithm for correcting multiple insertion-deletion errors in Helberg codes and their non-binary generalizations, extending a known algorithm for correcting multiple deletion errors.
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
The problem of correcting deletions and insertions has recently received significantly increased attention due to the DNA-based data storage technology, which suffers from deletions and insertions with extremely high probability. In this…
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…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
We introduce a fully constructive characterisation of holographic quantum error-correcting codes. That is, given a code and an erasure error we give a recipe to explicitly compute the terms in the RT formula. Using this formalism, we employ…
A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and…
A method to combine two quantum error-correcting codes is presented. Even when starting with additive codes, the resulting code might be non-additive. Furthermore, the notion of the erasure space is introduced which gives a full…
We present a decoder for nonbinary CWS quantum codes using the structure of union codes. The decoder runs in two steps: first we use a union of stabilizer codes to detect a sequence of errors, and second we build a new code, called union…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…