Results 281 to 290 of about 3,225,248 (329)

On Perfect Codes and Related Concepts

Designs, Codes and Cryptography, 2001
The concept of diameter perfect codes, which is a natural generalization of perfect codes (codes attaining the sphere-packing or Hamming bound), is introduced. The motivation for this work comes from the ``code-anticode'' bound of Delsarte in distance regular graphs.
Ahlswede, Rudolf, Aydinian, Haratyun, Khachatrian, Levon H.   +2 more
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Perfect byte-correcting codes

IEEE Transactions on Information Theory, 1998
Summary: We present a few new constructions for perfect linear single byte-correcting codes. These constructions generate some perfect single byte-correcting codes with new parameters, and some perfect single byte-correcting codes with known parameters and simpler presentation and implementation over the known codes. It is also shown that nonequivalent
exaly   +3 more sources

An enumeration of 1-perfect ternary codes

Discrete Mathematics, 2023
We study codes with parameters of the ternary Hamming $(n=(3^m-1)/2,3^{n-m},3)$ code, i.e., ternary $1$-perfect codes. The rank of the code is defined to be the dimension of its affine span.
Minjia Shi, Denis S Krotov
exaly   +3 more sources

MDS and I-Perfect Codes in Pomset Metric

IEEE Transactions on Information Theory, 2021
Recently pomset metric was introduced to accommodate Lee metric, thereby generalizing poset metrics for codes over $\mathbb {Z}_{{m}}$ . This work mainly studies results on Maximum distance separable (MDS) pomset codes and perfect codes over $\mathbb ...
Irrinki Gnana Sudha, Ramya Selvaraj
semanticscholar   +1 more source

Perfect codes in proper reduced power graphs of finite groups

, 2020
Let Γ be a graph with vertex set A subset C of is a perfect code of Γ if C is an independent set such that every vertex in is adjacent to exactly one vertex in C.
Xuanlong Ma
semanticscholar   +1 more source

Perfect Space–Time Block Codes [PDF]

IEEE Transactions on Information Theory, 2006
In this paper, we introduce the notion of perfect space-time block codes (STBC). These codes have full rate, full diversity, non-vanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and
Frédérique Oggier, Emanuele Viterbo
exaly   +2 more sources

Nonsystematic perfect codes

SIAM Journal on Discrete Mathematics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kevin T. Phelps, Mike LeVan
openaire   +1 more source

On Perfect Codes: Rank and Kernel

Designs, Codes and Cryptography, 2002
The rank of a nonlinear binary code \(C\) is the dimension of the subspace spanned by \(C\). The kernel of \(C\) is the largest possible linear code \(C'\) such that \(C\) can be obtained as a union of cosets of \(C'\). The authors study the problem of determining for what parameters \((r,k)\) there exists a perfect binary one-error-correcting code of ...
Kevin T. Phelps, Mercè Villanueva
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On non-full-rank perfect codes over finite fields

Designs, Codes and Cryptography, 2017
The paper deals with perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to a q-ary non-full-rank 1-perfect code of length n=(qm-1)/(q-1)\documentclass[12pt]{minimal ...
A. M. Romanov
semanticscholar   +1 more source

Linear Codes From Perfect Nonlinear Functions Over Finite Fields

IEEE Transactions on Communications, 2020
In this paper, a class of $p$ -ary 3-weight linear codes and a class of binary 2-weight linear codes are proposed respectively by virtue of the properties of the perfect nonlinear functions over $\mathbb {F}_{p^{m}}$ and $(m,s)$ -bent functions from
Yanan Wu, Nian Li, Xiangyong Zeng
semanticscholar   +1 more source