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A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Integer Codes
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2018/11/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Coding Theory
error-correcting codes, self-orthogonal codes, self-dual codes, codes over integer residue rings, Chinese remainder theorem,
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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.