The geometric structure of relative one-weight codes

Zihui Liu; Xiangyong Zeng

doi:10.3934/amc.2016011

The geometric structure of relative one-weight codes

Zihui Liu^*, Xiangyong Zeng

^*Corresponding author for this work

School of Mathematics and Statistics

Hubei University

Research output: Contribution to journal › Article › peer-review

Abstract

The geometric structure of any relative one-weight code is determined, and by using this geometric structure, the support weight distribution of subcodes of any relative one-weight code is presented. An application of relative one-weight codes to the wire-tap channel of type II with multiple users is given, and certain kinds of relative one-weight codes all of whose nonzero codewords are minimal are determined.

Original language	English
Pages (from-to)	367-377
Number of pages	11
Journal	Advances in Mathematics of Communications
Volume	10
Issue number	2
DOIs	https://doi.org/10.3934/amc.2016011
Publication status	Published - May 2016

Keywords

Geometric structure
Minimal codeword
Relative one-weight
Relative projective subspace
Support weight distribution

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10.3934/amc.2016011

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Liu, Z., & Zeng, X. (2016). The geometric structure of relative one-weight codes. Advances in Mathematics of Communications, 10(2), 367-377. https://doi.org/10.3934/amc.2016011

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abstract = "The geometric structure of any relative one-weight code is determined, and by using this geometric structure, the support weight distribution of subcodes of any relative one-weight code is presented. An application of relative one-weight codes to the wire-tap channel of type II with multiple users is given, and certain kinds of relative one-weight codes all of whose nonzero codewords are minimal are determined.",

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AB - The geometric structure of any relative one-weight code is determined, and by using this geometric structure, the support weight distribution of subcodes of any relative one-weight code is presented. An application of relative one-weight codes to the wire-tap channel of type II with multiple users is given, and certain kinds of relative one-weight codes all of whose nonzero codewords are minimal are determined.

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KW - Relative one-weight

KW - Relative projective subspace

KW - Support weight distribution

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The geometric structure of relative one-weight codes

Abstract

Keywords

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