Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices

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著者

    • SHIBUYA Tomoharu
    • Department of Information and Communication Sciences, Sophia University

抄録

Recently, Haley and Grant introduced the concept of <i>reversible codes</i> — a class of binary linear codes that can reuse the decoder architecture as the encoder and encodable by the iterative message-passing algorithm based on the <i>Jacobi method</i> over $\\mathbb{F}_2$. They also developed a procedure to construct parity check matrices of a class of reversible codes named <i>type-I</i> reversible codes by utilizing properties specific to circulant matrices. In this paper, we refine a mathematical framework for reversible codes based on circulant matrices through a ring theoretic approach. This approach enables us to clarify the necessary and sufficient condition on which type-I reversible codes exist. Moreover, a systematic procedure to construct all circulant matrices that constitute parity check matrices of type-I reversible codes is also presented.

収録刊行物

  • IEICE transactions on fundamentals of electronics, communications and computer sciences

    IEICE transactions on fundamentals of electronics, communications and computer sciences 94(11), 2121-2126, 2011-11-01

    The Institute of Electronics, Information and Communication Engineers

参考文献:  8件中 1-8件 を表示

各種コード

  • NII論文ID(NAID)
    10030191481
  • NII書誌ID(NCID)
    AA10826239
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    09168508
  • データ提供元
    CJP書誌  J-STAGE 
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