Self-dual skew-codes of odd lengths over $\mathbb {Z}_4+u\mathbb {Z}_4$

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发表日期：

2025年1月10日

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Saumya Shah,
Amit Sharma

摘要

In this paper, we first recall the skew cyclic codes of odd lengths over the ring $\mathbb {Z}_4+u\mathbb {Z}_4$ $Z_{4} + u Z_{4}$ with $u^2=1$ $u^{2} = 1$ as described in Shah and Sharma (2025). Using the generating set of these codes, we determine the generating set of their dual also. Subsequently, we give the conditions for these codes to be self-orthogonal and dual-containing. Additionally, we provide the necessary and sufficient conditions for these codes to be self-dual. We give some examples to illustrate these results. Also, we briefly discuss an application of these codes in constructing quantum codes.

Self-dual skew-codes of odd lengths over \(\mathbb {Z}_4+u\mathbb {Z}_4\)

摘要