The Geometry of Two-Weight Codes Over Zpm

被引：21

作者：

Shi, Minjia ^{[1
]}

Honold, Thomas ^{[2
]}

Sole, Patrick ^{[3
]}

Qiu, Yunzhen ^{[1
]}

Wu, Rongsheng ^{[1
]}

Sepasdar, Zahra ^{[4
]}

机构：

[1] Anhui Univ, Minist Educ, Sch Math Sci, Key Lab Intelligent Comp & Signal Proc, Hefei 230039, Anhui, Peoples R China

[2] Zhejiang Univ, ZJU UIUC Inst, Haining 314400, Peoples R China

[3] Aix Marseille Univ, CNRS, I2M, Cent Marseille, F-13009 Marseille, France

[4] Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad 9177948974, Razavi Khorasan, Iran

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Two-weight code; strongly regular graph; projective Hjelmslev geometry; cap; LINEAR CODES; ONE-WEIGHT; FAMILIES; RINGS;

D O I：

10.1109/TIT.2021.3114636

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We investigate fat projective linear codes over Z(pm), m >= 2, with two nonzero homogeneous weights ("two-weight codes"), building on the graph theory approach developed by Delsarte for codes over fields. Our main result is the classification of such codes under the additional assumption that the columns of a generator matrix of the code determine a cap in the projective Hjelmslev geometry PHG(k - 1, Z(pm)). This generalizes a result on projective two weight codes with dual distance at least four (Calderbank, 1982). The proof relies on a careful analysis of a certain strongly regular graph built on the cosets of the dual code, and on an interpretation of its parameters in terms of projective Hjelmslev geometry.

引用

页码：7769 / 7781

页数：13

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