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arXiv · 1401.6252

Note on the residue codes of self-dual $\mathbb{Z}_4$-codes having large minimum Lee weights

Masaaki Harada
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Abstract

It is shown that the residue code of a self-dual $\mathbb{Z}_4$-code of length $24k$ (resp.\ $24k+8$) and minimum Lee weight $8k+4 \text{ or }8k+2$ (resp.\ $8k+8 \text{ or }8k+6$) is a binary extremal doubly even self-dual code for every positive integer $k$. A number of new self-dual $\mathbb{Z}_4$-codes of length $24$ and minimum Lee weight $10$ are constructed using the above characterization. These codes are Type I $\mathbb{Z}_4$-codes having the largest minimum Lee weight and the largest Euclidean weight among all Type I $\mathbb{Z}_4$-codes of that length. In addition, new extremal Type II $\mathbb{Z}_4$-codes of length $56$ are found.

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Masaaki Harada. 2015-03-16. Note on the residue codes of self-dual $\mathbb{Z}_4$-codes having large minimum Lee weights. https://arxiv.org/abs/1401.6252

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