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Mathematics > Combinatorics

arXiv:1401.6252 (math)
[Submitted on 24 Jan 2014 (v1), last revised 16 Mar 2015 (this version, v3)]

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

Authors: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.
Comments: 18 pages
Subjects: Combinatorics (math.CO); Information Theory (cs.IT)
MSC classes: 94B05
Cite as: arXiv:1401.6252 [math.CO]
  (or arXiv:1401.6252v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1401.6252

Submission history

From: Masaaki Harada [view email]
[v1] Fri, 24 Jan 2014 03:48:41 UTC (15 KB)
[v2] Wed, 26 Mar 2014 02:55:22 UTC (17 KB)
[v3] Mon, 16 Mar 2015 10:20:26 UTC (17 KB)
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