The geometric structure of relative one-weight codes

Zihui  Liu; Xiangyong  Zeng

doi:10.3934/amc.2016011

Article Contents

2016, Volume 10, Issue 2: 367-377. Doi: 10.3934/amc.2016011

This issue Previous Article Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes Next Article Codes over local rings of order 16 and binary codes

The geometric structure of relative one-weight codes

Zihui Liu^1, and
Xiangyong Zeng^2,

1.
Department of Mathematics, Beijing Institute of Technology, Beijing, 100081
2.
Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, Hubei 430062

Received: June 30, 2014

Revised: July 31, 2015

Published: April 2016

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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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Mathematics Subject Classification: Primary: 94B05; Secondary: 94B05.

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