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Distance-preserving mappings (DPMs) are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of the same or longer length such that every two distinct vectors are mapped to permutations with the same or…
Quantum repeaters constitute a promising platform for enabling long distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An…
Quantum error correction (QEC) plays an essential role in fault-tolerantly realizing quantum algorithms of practical interest. Among different approaches to QEC, encoding logical quantum information in harmonic oscillator modes has been…
We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with…
Quantum error-correcting codes (QECCs) is at the heart of fault-tolerant quantum computing. As the size of quantum platforms is expected to grow, one of the open questions is to design new optimal codes of ever-increasing size. A related…
We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction applied to a permutation code. In particular, we show that a…
When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents…
The path toward practical superconducting quantum processors requires the integration of a large number of high-performance qubits. Modular architectures could offer a way to address the scaling limitations of monolithic designs by…
3GPP air interface standards support meter-level position location of a user in a cellular network. With wider bandwidths and narrow antenna beamwidths available at mmWave frequencies, cellular networks now have the potential to provide…
We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4),…
In the recent years, there has been active research on self-orthogonal embeddings of linear codes since they yielded some optimal self-orthogonal codes. LCD codes have a trivial hull so they are counterparts of self-orthogonal codes. So it…
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography.…
Frequency reuse in cells is one of the strategies that LTE uses to maximize the spectrum efficiency. However, it leads to an interference among the cells, especially at the cell edges where the probability for a cell-edge user to be…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
The scalability and interpretability of message-passing (MP) decoding, such as (quaternary) Belief Propagation, remain open challenges in quantum error correction. Even for surface codes, arguably the first testbed for decoding methods,…
Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle towards realizing…
Insertion-deletion codes (insdel codes for short) play an important role in synchronization error correction. The higher the minimum insdel distance, the more insdel errors the code can correct. Haeupler and Shahrasbi established the…
Deploying transformer models in practice is challenging due to their inference cost, which scales quadratically with input sequence length. To address this, we present a novel Learned Token Pruning (LTP) method which adaptively removes…