Results 21 to 30 of about 190,937 (260)
Minimal State-Space Representation of Convolutional Product Codes
Mathematics, 2021 In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes.
Joan-Josep Climent +3 more
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Combining hard and soft decoders for hypergraph product codes [PDF]
Quantum, 2021 Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF).
Antoine Grospellier +3 more
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A Modified Approach to Punctured Product Polar Codes
Journal of Telecommunications and Information Technology, 2019 A high-performance polar code introduced as a product polar code can be constructed by concatenating two short length polar codes. The punctured structure of this code was achieved by puncturing one of its constituent codes.
Mohammad Abu Hanif, Sina Vafi
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An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes [PDF]
MATEC Web of Conferences, 2021 In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes.
Yao Yu, Ma Yuena, Li Husheng, Lv Jingjie
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Matrix-Product Codes over Commutative Rings and Constructions Arising from σ,δ-Codes
Journal of Mathematics, 2021 A well-known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix-product code (MPC) is shown to remain valid over any commutative ring R.
Mhammed Boulagouaz, Abdulaziz Deajim
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Partitioning qubits in hypergraph product codes to implement logical gates [PDF]
Quantum, 2023 The promise of high-rate low-density parity check (LDPC) codes to substantially reduce the overhead of fault-tolerant quantum computation depends on constructing efficient, fault-tolerant implementations of logical gates on such codes.
Armanda O. Quintavalle +2 more
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Robust Locally Testable Codes and Products of Codes
Random Structures & Algorithms, 2004 AbstractWe continue the investigation of locally testable codes, i.e., error‐correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on local testability: First, motivated by the recently proposed notion of robust probabilistically checkable ...
Eli Ben-Sasson, Madhu Sudan 0001
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Entanglement-assisted Quantum Reed-Muller Tensor Product Codes [PDF]
QuantumWe present the construction of standard entanglement-assisted (EA) qubit Reed-Muller (RM) codes and their tensor product variants from classical RM codes. We show that the EA RM codes obtained using the CSS construction have zero coding rate and negative
Priya J. Nadkarni +3 more
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IEEE Transactions on Quantum Engineering, 2020 We provide a procedure to construct entanglement-assisted Calderbank-Shor-Steane (CSS) codes over qudits from the parity check matrices of two classical codes over Fq, where q = pk, p is prime, and k is a positive integer.
Priya J. Nadkarni +1 more
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Classical product code constructions for quantum Calderbank-Shor-Steane codes [PDF]
QuantumSeveral notions of code products are known in quantum error correction, such as hypergraph products, homological products, lifted products, balanced products, to name a few.
Dimiter Ostrev +3 more
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