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Applicable Algebra in Engineering, Communication and Computing
Erschienen in: Applicable Algebra in Engineering, Communication and Computing 2/2021

30.11.2019 | Original Paper

LCD codes from weighing matrices

verfasst von: Dean Crnković, Ronan Egan, B. G. Rodrigues, Andrea Švob

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 2/2021

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Abstract

Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order q using weighing matrices and their orbit matrices. The LCD codes constructed can be of any length dimension according to the choice of matrices used in their construction. As a special case, LCD codes of length 2n and dimension n are constructed which also have the property of being formally self-dual. Alternatively, under a condition depending on q that the codes are not LCD, this method constructs self-dual codes. To illustrate the method we construct LCD codes from weighing matrices, including the Paley conference matrices and Hadamard matrices. We also extend the construction to Hermitian LCD codes over the finite field of order 4. In addition, we propose a decoding algorithm that can be feasible for the LCD codes obtained from some of the given methods.
Vorheriger Artikel Complexity of deciding whether a tropical linear prevariety is a tropical variety

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Metadaten
Titel
LCD codes from weighing matrices
verfasst von
Dean Crnković
Ronan Egan
B. G. Rodrigues
Andrea Švob
Publikationsdatum
30.11.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Applicable Algebra in Engineering, Communication and Computing / Ausgabe 2/2021
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-019-00409-8

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