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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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
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Abstract 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.
AbstractList 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 𝔽n 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.
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 ð"½ and hyperinvariant subspaces of ð"½n 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.
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.
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 ¿ and hyperinvariant subspaces of ¿n 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. Peer Reviewed
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 and hyperinvariant subspaces of n 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.
Author Um, Laurence Emilie
Magret, Maria Dolors
García-Planas, María Isabel
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  givenname: Maria Dolors
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  givenname: Laurence Emilie
  surname: Um
  fullname: Um, Laurence Emilie
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  organization: Université Mohammed V-Agdal, Rabat, Morocco
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crossref_primary_10_1007_s10208_023_09609_8
crossref_primary_10_1016_j_jalgebra_2023_09_014
crossref_primary_10_1515_math_2021_0002
Cites_doi 10.1016/0024-3795(77)90032-5
10.1016/j.csi.2012.06.009
10.1016/j.laa.2008.09.036
10.1016/j.laa.2011.03.047
10.1016/0097-3165(82)90014-0
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Contributor Universitat Politècnica de Catalunya. SCL-EG - Sistemes de Control Lineals: estudi Geomètric
Universitat Politècnica de Catalunya. Departament de Matemàtiques
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Snippet 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...
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SubjectTerms 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
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Title Monomial codes seen as invariant subspaces
URI https://www.degruyter.com/doi/10.1515/math-2017-0093
https://www.proquest.com/docview/2545273923
https://recercat.cat/handle/2072/301181
https://doaj.org/article/56caf601192248699e79cc140d99e799
Volume 15
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