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Information 2018, 9(7), 172; https://doi.org/10.3390/info9070172

Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4)

School of Liberal Arts, KoreaTech, Cheonan 31253, Korea
Received: 23 June 2018 / Revised: 11 July 2018 / Accepted: 11 July 2018 / Published: 13 July 2018
(This article belongs to the Section Information Theory and Methodology)
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Abstract

Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over GF(2) and GF(4) with minimal shadow. In particular, we prove that there is no near-extremal Type I [24m,12m,2m+2] binary self-dual code with minimal shadow if m323, and we prove that there is no near-extremal Type I (6m+1,26m+1,2m+1) additive self-dual code over GF(4) with minimal shadow if m22. View Full-Text
Keywords: additive codes over GF(4); binary codes; extremal codes; minimal shadow; near-extremal codes; self-dual codes additive codes over GF(4); binary codes; extremal codes; minimal shadow; near-extremal codes; self-dual codes
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Han, S. Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4). Information 2018, 9, 172.

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