On perfect codes: Rank and kernel
type: Item
instance of: scholarly article
title: On perfect codes: Rank and kernel
zbMATH Open document ID: 1020.94028
DOI: 10.1023/A:1019936019517
author: M. Villanueva
author: Kevin T. Phelps
published in: Designs, Codes and Cryptography
publication date: 2003-04-03T00:00:00Z
review text: 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 length \(n = 2^m-1\), rank \(r\), and kernel dimension \(k\), and obtain several bounds on these parameters.
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 1892206
zbMATH Keywords: Hamming code
zbMATH Keywords: kernel
zbMATH Keywords: perfect code
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
full work available at URL: a:1019936019517
OpenAlex ID: W1519204501
Recommended article: On the ranks and kernels problem for perfect codes
Recommended article: On kernels of perfect codes
Recommended article: On rank and kernel of some mixed perfect codes
Recommended article: Q3148518
Recommended article: Full rank perfect codes and \(\alpha \)-kernels
Recommended article: On perfect codes in rank distance
Recommended article: Kernels and \(p\)-kernels of \(p^r\)-ary 1-perfect codes.
Recommended article: Rank and Kernel of Binary Hadamard Codes
Recommended article: On kernels and nuclei of rank metric codes
Recommended article: On full-rank perfect codes over finite fields
description: scientific article; zbMATH DE number 1892206