Almost affine codes
type: Item
instance of: scholarly article
title: Almost affine codes
zbMATH Open document ID: 0901.94024
DOI: 10.1023/A:1008244215660
author: Alexei Ashikhmin
author: Juriaan Simonis
published in: Designs, Codes and Cryptography
publication date: 1998-08-12T00:00:00Z
review text: Almost affine \(q\)-ary codes are codes having the property that puncturing in any set of positions results in a code for which the cardinality is a power of \(q\). The most obvious examples are cosets of linear codes. The matroid of an almost affine code is studied. An example is given of a matroid of an almost affine code that is not linearly representable. The connection between almost affine codes and perfect secret sharing schemes is given. It is reproved that binary and ternary almost affine codes are cosets of linear codes. The relation between an almost affine code and the dual of its matrix is explained, and results on the distance distribution and the dual distance distribution are obtained. Finally, the new concept of partial affine geometry is related to almost affine codes.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 51E25
zbMATH DE Number: 1164304
zbMATH Keywords: Delsarte inequalities
zbMATH Keywords: finite geometry
zbMATH Keywords: perfect secret sharing schemes
zbMATH Keywords: linear codes
zbMATH Keywords: matroid
zbMATH Keywords: distance distribution
zbMATH Keywords: partial affine geometry
reviewed by: L. M. G. M. Tolhuizen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1164304