Related papers: Quantum Constacyclic BCH Codes over Qudits: A Spec…
We present STFTCodec, a novel spectral-based neural audio codec that efficiently compresses audio using Short-Time Fourier Transform (STFT). Unlike waveform-based approaches that require large model capacity and substantial memory…
Full-rate space time codes (STC) with rate = number of transmit antennas have high multiplexing gain, but high decoding complexity even when decoded using reduced-complexity decoders such as sphere or QRDM decoders. In this paper, we…
In this paper, we study skew constacyclic codes over the ring $\mathbb{Z}_{q}R$ where $R=\mathbb{Z}_{q}+u\mathbb{Z}_{q}$, $q=p^{s}$ for a prime $p$ and $u^{2}=0$. We give the definition of these codes as subsets of the ring…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
In this paper, we study cyclic stabiliser codes over $\mathbb{F}_p$ of length dividing $p^t+1$ for some positive integer $t$. We call these $t$-Frobenius codes or just Frobenius codes for short. We give methods to construct them and show…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Let $\mathbb{Z}_p$ be the ring of integers modulo a prime number $p$ where $p-1$ is a quadratic residue modulo $p$. This paper presents the study of constacyclic codes over chain rings $\mathcal{R}=\frac{\mathbb{Z}_p[u]}{\langle…
Squeezed cat quantum error correction (QEC) codes have garnered attention because of their robustness against photon-loss and excitation errors while maintaining the biased-noise property of cat codes. In this work, we reveal the utility of…
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and…
This article presents new constructions of quantum error correcting Calderbank-Shor-Steane (CSS for short) codes. These codes are mainly obtained by Sloane's classical combinations of linear codes applied here to the case of self-orthogonal…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good.…
Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ where $p$ is an odd prime, $n$ be a positive integer satisfying ${\rm gcd}(n,p)=1$, and denote $R=\mathbb{F}_{p^m}[u]/\langle u^e\rangle$ where $e\geq 4$ be an even integer. Let…