Publication: An intrinsical description of group codes
Authors
Bernal Buitrago, José Joaquín ; Río Mateos, Ángel del ; Simón Pinero, Juan Jacobo
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Publisher
Springer
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DOI
https://doi.org/10.1007/s10623-008-9261-z
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info:eu-repo/semantics/article
Description
Abstract
A (left) group code of length n is a linear code which is the image of a (left) ideal of
a group algebra via an isomorphism FG → Fn which maps G to the standard basis of Fn. Many
classical linear codes have been shown to be group codes. In this paper we obtain a criterion to
decide when a linear code is a group code in terms of its intrinsical properties in the ambient
space Fn, which does not assume an “a priori” group algebra structure on Fn. As an application
we provide a family of groups (including metacyclic groups) for which every two-sided group
code is an abelian group code.
It is well known that Reed-Solomon codes are cyclic and its parity check extensions are
elementary abelian group codes. These two classes of codes are included in the class of Cauchy
codes. Using our criterion we classify the Cauchy codes of some lengths which are left group
codes and the possible group code structures on these codes.
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Citation
Designs, codes and Cryptography Volume 51, pages 289–300, (2009)
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