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Related papers: Johnson Type Bounds on Constant Dimension Codes

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We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum…

Quantum Physics · Physics 2022-12-09 Anthony Leverrier , Gilles Zémor

Deterministic identification (DI) for the discrete-time Poisson channel, subject to an average and a peak power constraint, is considered. It is established that the code size scales as $2^{(n\log n)R}$, where $n$ and $R$ are the block…

Information Theory · Computer Science 2021-09-29 Mohammad J. Salariseddigh , Uzi Pereg , Holger Boche , Christian Deppe , Robert Schober

We consider a block fading additive white Gaussian noise (AWGN) channel with perfect channel state information (CSI) at the transmitter and the receiver. First, for a given codeword length and non-vanishing average probability of error, we…

Information Theory · Computer Science 2019-04-10 Deekshith P K , K Gautam Shenoy , Vinod Sharma

This paper studies the third-order characteristic of nonsingular discrete memoryless channels and the Gaussian channel with a maximal-power constraint. The third-order term in our expansions employs a new quantity here called the channel…

Information Theory · Computer Science 2024-08-23 Recep Can Yavas , Victoria Kostina , Michelle Effros

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…

Quantum Physics · Physics 2009-11-13 Dan Hu , Weidong Tang , Meisheng Zhao , Qing Chen , Sixia Yu , C. H. Oh

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.

Information Theory · Computer Science 2014-06-20 Anna-Lena Trautmann

Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…

Information Theory · Computer Science 2013-05-23 Johan P. Hansen

By a famous result of Doyen, Hubaut and Vandensavel \cite{DHV}, the 2-rank of a Steiner triple system on $2^n-1$ points is at least $2^n -1 -n$, and equality holds only for the classical point-line design in the projective geometry…

Combinatorics · Mathematics 2018-08-07 Dieter Jungnickel , Vladimir D. Tonchev

The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The…

Information Theory · Computer Science 2020-08-18 Yuta Sakai , Vincent Y. F. Tan , Mladen Kovačević

We generalize the fundamental bounds of Delsarte thesis (1973) on codes of given degree and designs of given strength in the new setting of Bannai et al. (2025). We assume the scheme is weakly metric in the sense of (Sol\'e, 1989). We give…

Combinatorics · Mathematics 2026-05-29 Minjia Shi , Jing Wang , Patrick Solé

The two-user broadcast channel (BC) with receivers connected by bidirectional cooperation links of finite capacities, known as conferencing decoders, is considered. A novel capacity region outer bound is established based on multiple…

Information Theory · Computer Science 2025-08-12 Reza K. Farsani , Wei Yu

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper…

Information Theory · Computer Science 2010-11-09 Kenneth W. Shum , Wing Shing Wong , Chung Shue Chen

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…

Optimization and Control · Mathematics 2023-03-28 Marek Tyburec , Jan Zeman

In this paper, we give upper bounds on the sizes of $(d, L)$ list-decodable codes in the Hamming metric space from covering codes with the covering radius smaller than or equal to $d$. When the list size $L$ is $1$, this gives many new…

Information Theory · Computer Science 2023-01-25 Hao Chen , Longjiang Qu , Chengju Li , Shanxiang Lyu , Liqing Xu

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…

Information Theory · Computer Science 2014-03-12 Bocong Chen , San Ling , Guanghui Zhang

In this paper, a construction of constant weight codes based on the unique decomposition of elements in lattices is presented. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed…

Information Theory · Computer Science 2013-04-30 Anirban Ghatak

In network communications, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. The investigation of performance bounds on the numbers of…

Information Theory · Computer Science 2015-05-07 Xuan Guang , Jiyong Lu , Fang-Wei Fu

We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…

Information Theory · Computer Science 2020-10-15 Arman Fazeli , S. Hamed Hassani , Marco Mondelli , Alexander Vardy

We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability,…

Information Theory · Computer Science 2020-08-18 MohammadReza Ebrahimi , Farshad Lahouti , Victoria Kostina

Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…

Quantum Physics · Physics 2008-11-11 Salah A. Aly , Andreas Klappenecker