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For a prime p and \(\ell \in \mathbb {N}\) with \(\gcd (\ell,p) = 1\) , this work explores the hulls of \(\ell \) -length cyclic codes over \(\mathbb {Z}_{p^3}\) . We establish the form of the generators of the hulls and provide a characterization of the hulls. Further, we present a condition for these codes to be LCD. To formulate the p-dimensions of the hulls, first, we find the types of the hulls and then use them to come up with an expression for the p-dimensions of the hulls. Moreover, for a fixed p-dimension of the hull, we count all the cyclic codes.

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Hulls of Cyclic Codes Over a Local Ring

  • 会议论文

  • 发表日期：

    2026年

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  • Indibar Debnath,
  • Om Prakash

摘要

For a prime p and \(\ell \in \mathbb {N}\) with \(\gcd (\ell,p) = 1\) , this work explores the hulls of \(\ell \) -length cyclic codes over \(\mathbb {Z}_{p^3}\) . We establish the form of the generators of the hulls and provide a characterization of the hulls. Further, we present a condition for these codes to be LCD. To formulate the p-dimensions of the hulls, first, we find the types of the hulls and then use them to come up with an expression for the p-dimensions of the hulls. Moreover, for a fixed p-dimension of the hull, we count all the cyclic codes.