A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Integer Codes

Hajime MATSUI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.11   pp.1952-1956
Publication Date: 2018/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1952
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
error-correcting codes,  self-orthogonal codes,  self-dual codes,  codes over integer residue rings,  Chinese remainder theorem,  

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Summary: 
Integer codes are defined by error-correcting codes over integers modulo a fixed positive integer. In this paper, we show that the construction of integer codes can be reduced into the cases of prime-power moduli. We can efficiently search integer codes with small prime-power moduli and can construct target integer codes with a large composite-number modulus. Moreover, we also show that this prime-factorization reduction is useful for the construction of self-orthogonal and self-dual integer codes, i.e., these properties in the prime-power moduli are preserved in the composite-number modulus. Numerical examples of integer codes and generator matrices demonstrate these facts and processes.