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<p>In this article, we introduce new scalar products over finite rings via additive isomorphisms. This allows us to define new notions of right (respectively, left) orthogonal codes, that are not necessarily linear. This leads to definitions of right (respectively, left) dual codes and left LCD codes similar to the classical LCD codes. Furthermore, we provide necessary and sufficient conditions for the existence of these codes.</p>

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Scalar products and Left LCD codes

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Nabil Bennenni,
  • André Leroy

摘要

In this article, we introduce new scalar products over finite rings via additive isomorphisms. This allows us to define new notions of right (respectively, left) orthogonal codes, that are not necessarily linear. This leads to definitions of right (respectively, left) dual codes and left LCD codes similar to the classical LCD codes. Furthermore, we provide necessary and sufficient conditions for the existence of these codes.