New binary and ternary LCD codes

Carlos  Galindo; Hans Olav Geil; Fernando Hernando; Diego Ruano Benito

doi:10.1109/TIT.2018.2834500

New binary and ternary LCD codes

Carlos Galindo, Hans Olav Geil, Fernando Hernando, Diego Ruano Benito

Research output: Contribution to journal › Journal article › Research › peer-review

15 Citations (Scopus)

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Abstract

LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield-subcodes of J-affine variety codes are a generalization of BCH codes which have been successfully used for constructing good quantum codes. We describe binary and ternary LCD codes constructed as subfieldsubcodes of J-affine variety codes and provide some new and good LCD codes coming from this construction.

Original language	English
Article number	8356685
Journal	I E E E Transactions on Information Theory
Volume	65
Issue number	2
Pages (from-to)	1008-1016
Number of pages	9
ISSN	0018-9448
DOIs	https://doi.org/10.1109/TIT.2018.2834500
Publication status	Published - 1 Feb 2019

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title = "New binary and ternary LCD codes",

abstract = "LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield-subcodes of J-affine variety codes are a generalization of BCH codes which have been successfully used for constructing good quantum codes. We describe binary and ternary LCD codes constructed as subfieldsubcodes of J-affine variety codes and provide some new and good LCD codes coming from this construction.",

keywords = "LCD codes, complementary dual, subfieldsubcodes, J-affine variety codes, toric codes, Liquid crystal displays, linear codes",

author = "Carlos Galindo and Geil, {Hans Olav} and Fernando Hernando and {Ruano Benito}, Diego",

year = "2019",

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doi = "10.1109/TIT.2018.2834500",

language = "English",

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T1 - New binary and ternary LCD codes

AU - Galindo, Carlos

AU - Geil, Hans Olav

AU - Hernando, Fernando

AU - Ruano Benito, Diego

PY - 2019/2/1

Y1 - 2019/2/1

N2 - LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield-subcodes of J-affine variety codes are a generalization of BCH codes which have been successfully used for constructing good quantum codes. We describe binary and ternary LCD codes constructed as subfieldsubcodes of J-affine variety codes and provide some new and good LCD codes coming from this construction.

AB - LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield-subcodes of J-affine variety codes are a generalization of BCH codes which have been successfully used for constructing good quantum codes. We describe binary and ternary LCD codes constructed as subfieldsubcodes of J-affine variety codes and provide some new and good LCD codes coming from this construction.

KW - LCD codes

KW - complementary dual

KW - subfieldsubcodes

KW - J-affine variety codes

KW - toric codes

KW - Liquid crystal displays

KW - linear codes

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DO - 10.1109/TIT.2018.2834500

M3 - Journal article

SN - 0018-9448

VL - 65

SP - 1008

EP - 1016

JO - I E E E Transactions on Information Theory

JF - I E E E Transactions on Information Theory

IS - 2

M1 - 8356685

ER -

New binary and ternary LCD codes

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