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01.03.2015 | Ausgabe 3/2015

Designs, Codes and Cryptography 3/2015

On generator matrices and parity check matrices of generalized integer codes

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 3/2015
Autor:
Hajime Matsui
Wichtige Hinweise
Communicated by C. Carlet.

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.

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