Paper Info
Title
On generator matrices and parity check matrices of generalized integer codes
Abstract
Generalized integer codes are defined as codes over rings of integers modulo $$n$$ 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.
Year
DOI
Venue
2015
10.1007/s10623-013-9883-7
Designs, Codes and Cryptography
Keywords
DocType
Volume
Codes over rings,Elementary divisors,Extended Euclidean algorithm,Bézout’s identity,Integer lattices,Hecke rings,94B05,94B25,94B40,94B60,11T71
Journal
74
Issue
ISSN
Citations 
3
0925-1022
2
PageRank 
References 
Authors
0.41
21
1
Name
Order
Citations
PageRank
Hajime Matsui1188.14