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<p>Formally self-dual (FSD) codes and hulls of linear codes have recently gained significant attention due to their profound theoretical implications and practical applications. Concerns have also been raised regarding FSD codes with small hulls. However, limited attention has been given to the construction of linear codes with hulls of arbitrary dimensions. In this paper, we investigate the hulls of circulant and negacirculant codes with low indices, and provide a characterization of the necessary and sufficient conditions for these codes to achieve desirable hull dimensions with respect to both Euclidean and Hermitian inner products, in terms of their eigenvalues. This work contributes to the improvement and extension of existing results. Building on these findings, we identify numerous new or enhanced FSD codes with desirable hull dimensions, comparing them to the best-known codes in the literature.</p>

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Formally self-dual codes with desirable hull dimensions

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Xia Zhang,
  • Gang Wang,
  • Yan Liu

摘要

Formally self-dual (FSD) codes and hulls of linear codes have recently gained significant attention due to their profound theoretical implications and practical applications. Concerns have also been raised regarding FSD codes with small hulls. However, limited attention has been given to the construction of linear codes with hulls of arbitrary dimensions. In this paper, we investigate the hulls of circulant and negacirculant codes with low indices, and provide a characterization of the necessary and sufficient conditions for these codes to achieve desirable hull dimensions with respect to both Euclidean and Hermitian inner products, in terms of their eigenvalues. This work contributes to the improvement and extension of existing results. Building on these findings, we identify numerous new or enhanced FSD codes with desirable hull dimensions, comparing them to the best-known codes in the literature.