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Consider the identification (ID) via channels problem, where a receiver wants to decide whether the transmitted identifier is its identifier, rather than decoding the identifier. This model allows to transmit identifiers whose size scales…

Information Theory · Computer Science 2021-06-28 Onur Günlü , Joerg Kliewer , Rafael F. Schaefer , Vladimir Sidorenko

The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…

Quantum Physics · Physics 2026-03-06 Andrey Boris Khesin , Jonathan Z. Lu

Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…

Information Theory · Computer Science 2015-04-14 Eli Ben-Sasson , Tuvi Etzion , Ariel Gabizon , Netanel Raviv

In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves the base $2$ expansion of the integers in their defining…

Information Theory · Computer Science 2023-09-22 Minjia Shi , Sihui Tao , Jon-Lark Kim , Patrick Sole

Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes,…

Information Theory · Computer Science 2012-02-07 Sunghyu Han , Jon-Lark Kim

Recent work has shown that properly designed protograph-based LDPC codes may have minimum distance linearly increasing with block length. This notion rests on ensemble arguments over all possible expansions of the base protograph. When…

Information Theory · Computer Science 2012-02-17 Brian K. Butler , Paul H. Siegel

Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…

Quantum Physics · Physics 2014-11-17 Yuichiro Fujiwara , Peter Vandendriessche

In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed…

Information Theory · Computer Science 2016-11-17 Dung Viet Nguyen , Bane Vasic , Michael W. Marcellin

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…

Information Theory · Computer Science 2017-07-17 Bocong Chen , Hongwei Liu

Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights…

Information Theory · Computer Science 2020-07-23 Guangkui Xu , Xiwang Cao

Self-dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta-dihedral in odd characteristic. Exact counting formulae are derived for them and used to show they contain families of codes with…

Information Theory · Computer Science 2016-03-03 Adel Alahmadi , Funda Özdemir , Patrick Solé

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…

Combinatorics · Mathematics 2020-11-20 Masaaki Harada , Ken Saito

Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and…

Information Theory · Computer Science 2024-05-24 Hao Chen , Conghui Xie , Cunsheng Ding

Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first…

Information Theory · Computer Science 2013-09-06 Nian Li , Chunlei Li , Tor Helleseth , Cunsheng Ding , Xiaohu Tang

Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent…

Information Theory · Computer Science 2024-03-20 Jiaxin Wang , Yadi Wei , Fang-Wei Fu , Juan Li

Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic…

Information Theory · Computer Science 2016-04-20 Yun Fan , Liang Zhang

This paper proposes an algorithm to search a family of multiple sets of minimum correlated one dimensional uni-polar (optical) orthogonal codes (1-DUOC) or optical orthogonal codes (OOC) with fixed as well as variable code parameters. The…

Information Theory · Computer Science 2024-11-12 Ram Chandra Singh Chauhan , Yatindra Nath Singh , Rachna Asthana

Let $\mathbb{F}_q$ be a finite field of order $q$, a prime power integer such that $q=et+1$ where $t\geq 1,e\geq 2$ are integers. In this paper, we study cyclic codes of length $n$ over a non-chain ring $R_{e,q}=\mathbb{F}_q[u]/\langle…

Information Theory · Computer Science 2021-06-16 Habibul Islam , Edgar Martínez-Moro , Om Prakash

Non-binary linear block codes (NB-LBCs) are an important class of error-correcting codes that are especially competent in correcting burst errors. They have broad applications in modern communications and storage systems. However, efficient…

Information Theory · Computer Science 2026-01-21 Jingyu Lin , Li Chen , Xiaoqian Ye

We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise…

Information Theory · Computer Science 2014-06-19 Claude Carlet , Finley Freibert , Sylvain Guilley , Michael Kiermaier , Jon-Lark Kim , Patrick Solé