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arXiv · 1811.10991

An explicit representation and enumeration for negacyclic codes of length $2^kn$ over $\mathbb{Z}_4+u\mathbb{Z}_4$

Yonglin Cao·Yuan Cao·Rama Krishna Bandi·Fang-Wei Fu
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Abstract

In this paper, an explicit representation and enumeration for negacyclic codes of length $2^kn$ over the local non-principal ideal ring $R=\mathbb{Z}_4+u\mathbb{Z}_4$ $(u^2=0)$ is provided, where $k, n$ are any positive integers and $n$ is odd. As a corollary, all distinct negacyclic codes of length $2^k$ over $R$ are listed precisely. Moreover, a mass formula for the number of negacyclic codes of length $2^kn$ over $R$ is given and a mistake in [Cryptogr. Commun. (2017) 9: 241--272] is corrected.

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Yonglin Cao, Yuan Cao, Rama Krishna Bandi, Fang-Wei Fu. 2019-03-18. An explicit representation and enumeration for negacyclic codes of length $2^kn$ over $\mathbb{Z}_4+u\mathbb{Z}_4$. https://arxiv.org/abs/1811.10991

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