Monomial codes seen as invariant subspaces

It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Vol. 15; no. 1; pp. 1099 - 1107
Main Authors: García-Planas, María Isabel, Magret, Maria Dolors, Um, Laurence Emilie
Format: Journal Article Publication
Language:English
Published: Warsaw De Gruyter Open 01.01.2017
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
De Gruyter
Subjects:
15 Linear and multilinear algebra; matrix theory
15B33
94 Information And Communication, Circuits
94B Theory of error-correcting codes and error-detecting codes
94B15
Anells (Àlgebra)
Binary system
Classificació AMS
Codificació, Teoria de la
Coding theory
Fields (mathematics)
Invariant subspaces
Invariants
Linear algebra
Linear transformations
Matemàtiques i estadística
Monomial codes
Rings (Algebra)
Subspaces
Àrees temàtiques de la UPC
ISSN:2391-5455, 2391-5455
Online Access:Get full text
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Summary:It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field 𝔽 and hyperinvariant subspaces of 𝔽 under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.
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ISSN:2391-5455
2391-5455
DOI:10.1515/math-2017-0093