A binary perfect code of length 15 and codimension 0
type: Item
instance of: scholarly article
title: A binary perfect code of length 15 and codimension 0
zbMATH Open document ID: 0802.94021
DOI: 10.1007/BF01388453
author: Olof Heden
published in: Designs, Codes and Cryptography
publication date: 1994-12-15T00:00:00Z
review text: Let \(C\) be a perfect binary nonlinear single error correcting code of length 15. The kernel of \(C\) is defined as \(\ker(C)= \{v\in F_ 2^{15}\mid v+c\in C\) for every element \(c\in C\}\) where \(F_ 2\) is the field of two elements. Let \(\langle C\rangle^ \perp\) denote the orthogonal code, the set of all elements of \(F_ 2^{15}\) orthogonal to all elements of \(C\). The codimension of \(C\), \(\text{cdim}(C)\), is the dimension of \(\langle C\rangle^ \perp\). Three new perfect single error correcting codes, \(C_ i\), are constructed with \(\dim (\ker (C_ i)) =i\), \(i=1,2,3\). It follows that the codimension of \(C_ 1\) is zero. The construction uses MDS codes of length 4, dimension 3 over \(F_ 4\).
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 597832
zbMATH Keywords: nonlinear binary codes
zbMATH Keywords: perfect codes
zbMATH Keywords: error correcting code
reviewed by: Ian Blake
MaRDI profile type: Publication
cites work: Q3701331
cites work: A General Product Construction for Error Correcting Codes
cites work: An algebraic study of group and nongroup error-correcting codes
cites work: A Combinatorial Construction of Perfect Codes
cites work: Q3325636
cites work: A new construction of group and nongroup perfect codes
description: scientific article; zbMATH DE number 597832