Related papers: Quasi-twisted codes: decoding and applications in …
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes…
For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based…
We study complementary information set codes of length $tn$ and dimension $n$ of order $t$ called ($t-$CIS code for short). Quasi-cyclic and quasi-twisted $t$-CIS codes are enumerated by using their concatenated structure. Asymptotic…
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic…
Recent results of Kaplan et al., building on previous work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems can be completely broken by quantum chosen-plaintext attacks (qCPA). In such…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…
This paper presents a novel post-quantum cryptosystem based on high-memory masked convolutional codes. Unlike conventional code-based schemes that rely on block codes with fixed dimensions and limited error-correction capability, our…
This article defines multi-twisted Goppa (MTG) codes as subfield subcodes of duals of multi-twisted Reed-Solomon (MTRS) codes and examines their properties. We show that if $t$ is the degree of the MTG polynomial defining an MTG code, its…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a…
It is a major challenge to construct good quantum codes supporting fault-tolerant (e.g. transversal) non-Clifford gates with low-weight parity-check measurements. In this paper, we construct the first known quantum codes with linear…
The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear complementary pairs of quasi-cyclic and quasi-twisted codes…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
Recently an algorithm has been constructed that shows the binary icosahedral group $\2I$ together with a $T$-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code…
A new lower bound on the minimum Hamming distance of linear quasi-cyclic codes over finite fields is proposed. It is based on spectral analysis and generalizes the Semenov- Trifonov bound in a similar way as the Hartmann-Tzeng bound extends…
We present a new family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasi-cyclic codes. The codes are defined using a pair of integers $(r,s)$ and…
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine…