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<p>Entanglement-assisted quantum error-correcting (EAQEC) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, we first give a <i>s</i>-Galois LCD codes decomposition of linear codes over finite fields. By means of this decomposition of cyclic codes and matrix-product codes, we provide two methods to construct EAQEC codes, and we find new EAQEC codes. In addition, our EAQEC codes have improved parameters (e.g., higher minimum distance or greater dimension).</p>

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Galois LCD codes decomposition of linear codes and their applications to EAQEC codes

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Hui Li,
  • Xiusheng Liu

摘要

Entanglement-assisted quantum error-correcting (EAQEC) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, we first give a s-Galois LCD codes decomposition of linear codes over finite fields. By means of this decomposition of cyclic codes and matrix-product codes, we provide two methods to construct EAQEC codes, and we find new EAQEC codes. In addition, our EAQEC codes have improved parameters (e.g., higher minimum distance or greater dimension).