Results 11 to 20 of about 29,686,764 (312)
Good Quantum LDPC Codes with Linear Time Decoders [PDF]
Symposium on the Theory of Computing, 2022 We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain (2m× m)V →δ0 (2m)E →δ1 2F where V (X-checks) are the vertices, E (qubits) are ...
Irit Dinur +3 more
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Two families of negacyclic BCH codes [PDF]
Designs, Codes and Cryptography, 2022 Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let q be an odd prime power and m be a positive integer.
Xiaoqiang Wang, Zhonghua Sun, C. Ding
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Reed–Muller Codes: Theory and Algorithms [PDF]
IEEE Transactions on Information Theory, 2020 Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science.
E. Abbe, Amir Shpilka, Min Ye
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New quantum codes from constacyclic codes over the ring Rk, m
Advances in Mathematics of Communications, 2022 For any odd prime \begin{document}$ p $\end{document} , we study constacyclic codes of length \begin{document}$ n $\end{document} over the finite commutative non-chain ring \begin{document}$ R_{k,m} = \mathbb{F}_{p^m}[u_1,u_2,\dots,u_k]/\langle u^2_i-1 ...
H. Islam, O. Prakash, Ram Krishna Verma
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Surface codes: Towards practical large-scale quantum computation [PDF]
, 2012 This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers ...
A. Fowler +3 more
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Codes for Natural History Collections in Ichthyology and Herpetology
Copeia, 2020 Assembled here is a reasonably complete list of annotated codes for historical and modern natural history collections associated with lost and extant specimens of fossil and Recent fishes, amphibians, and reptiles.
M. Sabaj
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Near MDS codes from oval polynomials [PDF]
Discrete Mathematics, 2020 A linear code with parameters of the form $[n, k, n-k+1]$ is referred to as an MDS (maximum distance separable) code. A linear code with parameters of the form $[n, k, n-k]$ is said to be almost MDS (i.e., almost maximum distance separable) or AMDS for ...
Qiuyan Wang, Ziling Heng
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Optimal Binary Linear Codes From Maximal Arcs [PDF]
IEEE Transactions on Information Theory, 2020 The binary Hamming codes with parameters $[{2^{m}-1, 2^{m}-1-m, 3}]$ are perfect. Their extended codes have parameters $[{2^{m}, 2^{m}-1-m, 4}]$ and are distance-optimal.
Ziling Heng, C. Ding, Weiqiong Wang
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Hermitian Rank Metric Codes and Duality
IEEE Access, 2021 In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for $\mathbb {F}_{q^{2}}$ -linear matrix codes in the ambient space $(\mathbb {F}_{q^{2}})_{n,m}$ and for both $\mathbb {F}_{q^{2}}$ -additive ...
Javier De La Cruz +2 more
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On $m$-dimensional toric codes
CoRR, 2005 17 pages, 4 figures; typos ...
John Little, Ryan Schwarz
openaire +2 more sources