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<p>In this paper, we use generalized Reed–Solomon (GRS) codes as block codes to construct classical convolutional codes and classical convolutional GRS codes with arbitrary memory and flexible degrees are derived. Particularly, for unit-memory and double-memory, some of the convolutional GRS codes are exactly convolutional maximum-distance-separable (MDS) codes. From the resulting convolutional GRS codes, under Euclidean and Hermitian inner products, quantum convolutional codes are obtained, respectively. A connection between quantum convolutional codes and GRS codes is also established.</p>

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Classical convolutional GRS codes and applications to quantum convolutional codes

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Xiujing Zheng,
  • Liqi Wang,
  • Shixin Zhu,
  • Ruhao Wan

摘要

In this paper, we use generalized Reed–Solomon (GRS) codes as block codes to construct classical convolutional codes and classical convolutional GRS codes with arbitrary memory and flexible degrees are derived. Particularly, for unit-memory and double-memory, some of the convolutional GRS codes are exactly convolutional maximum-distance-separable (MDS) codes. From the resulting convolutional GRS codes, under Euclidean and Hermitian inner products, quantum convolutional codes are obtained, respectively. A connection between quantum convolutional codes and GRS codes is also established.