English
Related papers

Related papers: Multiply Constant-Weight Codes and the Reliability…

200 papers

In this paper, we present two constructions of quantum locally testable codes (QLTC) with constant soundness. In the first approach, we introduce an operation called check product, and show how this operation gives rise to QLTCs of constant…

Information Theory · Computer Science 2024-10-23 Andrew Cross , Zhiyang He , Anand Natarajan , Mario Szegedy , Guanyu Zhu

Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental…

Quantum Physics · Physics 2026-01-23 Lily Wang , Andy Zeyi Liu , Ray Li , Aleksander Kubica , Shouzhen Gu

In this paper, we further extend the study of function-correcting codes in the homogeneous metric over a chain ring $\mathbb{Z}_{2^s}$ for broader classes of functions, namely, locally bounded functions and linear functions, and for weight…

Information Theory · Computer Science 2026-03-17 Gyanendra K. Verma , Abhay Kumar Singh

A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length…

Information Theory · Computer Science 2009-01-12 Eric Z. Chen

The study of codes for powerlines communication has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the…

Information Theory · Computer Science 2012-08-29 Yeow Meng Chee , Han Mao Kiah , Punarbasu Purkayastha

The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes…

Information Theory · Computer Science 2025-10-14 Zicheng Ye , Yuan Li , Zhichao Liu , Huazi Zhang , Jun Wang , Guiying Yan , Zhiming Ma

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…

Information Theory · Computer Science 2012-06-22 Cunsheng Ding

We show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously…

Information Theory · Computer Science 2023-08-11 Gleb Kalachev , Pavel Panteleev

During the last years, Physically Unclonable Functions (PUFs) have become a very important research area in the field of hardware security due to their capability of generating volatile secret keys as well as providing a low-cost…

Cryptography and Security · Computer Science 2024-02-15 M. Garcia-Bosque , G. Díez-Señorans , C. Sánchez-Azqueta , S. Celma

Subspace codes, i.e., sets of subspaces of $\mathbb{F}_q^v$, are applied in random linear network coding. Here we give improved upper bounds for their cardinalities based on the Johnson bound for constant dimension codes.

Combinatorics · Mathematics 2019-01-17 Thomas Honold , Michael Kiermaier , Sascha Kurz

Physical unclonable functions (PUFs) are small circuits that are widely used as hardware security primitives for authentication. These circuits can generate unique signatures because of the inherent randomness in manufacturing and process…

Emerging Technologies · Computer Science 2020-08-11 Lulu Ge , Keshab K. Parhi

We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…

Combinatorics · Mathematics 2014-09-17 Chao Tian , Vinay A. Vaishampayan , N. J. A. Sloane

In this paper, an algebraic binning based coding scheme and its associated achievable rate for key generation using physically unclonable functions (PUFs) is determined. This achievable rate is shown to be optimal under the generated-secret…

Information Theory · Computer Science 2018-02-08 Yitao Chen , Muryong Kim , Sriram Vishwanath

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…

Information Theory · Computer Science 2021-02-22 Whan-Hyuk Choi , Jon-Lark Kim

The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of…

Information Theory · Computer Science 2020-02-27 Onur Günlü , Onurcan İşcan , Vladimir Sidorenko , Gerhard Kramer

We introduce a class of bosonic quantum error-correcting codes, termed \emph{extended binomial codes}, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are…

Quantum Physics · Physics 2025-09-11 En-Jui Chang

We present an encoding and decoding scheme for constant weight sequences, that is, given an information sequence, the construction results in a sequence of specific weight within a certain range. The scheme uses a prefix design that is…

Information Theory · Computer Science 2017-06-06 Elie Ngomseu Mambou , Theo G. Swart

Constant dimension codes are e.g. used for error correction and detection in random linear network coding, so that constructions for these codes have achieved wide attention. Here, we improve over 150 lower bounds by describing better…

Information Theory · Computer Science 2020-04-30 Sascha Kurz

The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in $\GF(q^m)$. The proposed explicit construction of expanded generator matrix and expanded parity check matrix…

Information Theory · Computer Science 2008-07-08 Yingquan Wu

This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…

Information Theory · Computer Science 2007-10-15 Russell Bent , Michael Schear , Lane A. Hemaspaandra , Gabriel Istrate