A Note on New Near-Extremal Type I Z4-Codes of Length 48

被引：0

作者：

Mravic, Matteo ^{[1
]}

Rukavina, Sanja ^{[1
]}

机构：

[1] Univ Rijeka, Fac Math, Rijeka 51000, Croatia

来源：

MATHEMATICS | 2025年 / 13卷 / 06期

关键词：

Z(4)-code; Euclidean weight; self-dual code; Type I Z(4)-code; near-extremal <mml:semantics><mml:msub>Z<mml:mn>4</mml:mn></mml:msub></mml:semantics>-code; SELF-DUAL CODES; Z(4) CODES;

D O I：

10.3390/math13060946

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The subject of this work is self-dual Type I Z(4)-codes of length 48. It is known that the usual upper bound for the minimum Euclidean weight for the self-dual Z4-codes cannot be achieved for this length and type of codes; i.e., extremal Type I Z(4)-codes of length 48 do not exist. We are therefore looking for near-extremal Type I Z(4)-codes of length 48. The only known Type I near-extremal Z(4)-code of length 48 was constructed in 2015 by M. Harada. We adapted a known pseudo-random search method and found at least two new near-extremal Type I Z(4)-codes of length 48. These codes are the first Type I near-extremal Z(4)-codes with a residue code of minimum weight 8.

引用

页数：10

共 29 条

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2012, 349 (09): : 2824 - 2833
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Masaaki Harada
Ching Hung Lam
Akihiro Munemasa
Mathematische Zeitschrift, 2013, 274 (1-2) : 685 - 700

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