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Designs, Codes and Cryptography

Erschienen in:

01.03.2015

On generator matrices and parity check matrices of generalized integer codes

verfasst von: Hajime Matsui

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2015

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Abstract

Generalized integer codes are defined as codes over rings of integers modulo \(n\) in which individual code symbols generally have different moduli. In this paper, we use a certain type of matrix identities to derive a necessary and sufficient condition for integer matrices to be equal to the generator matrices of generalized integer codes. Moreover, it is shown that the parity check matrix is generated from this matrix identity of the generator matrix. We also show the close connection between the listing of a certain type of integer codes and Hecke rings. Finally, an efficient algorithm that enumerates theoretically all of the generator matrices of generalized integer codes is provided.

Vorheriger Artikel New extremal binary self-dual codes of length 64 from -lifts of the extended binary Hamming code

Nächster Artikel On the linear complexity of Legendre–Sidelnikov sequences

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Titel: On generator matrices and parity check matrices of generalized integer codes
verfasst von: Hajime Matsui
Publikationsdatum: 01.03.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9883-7

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