On the third greedy weight of 4-dimensional codes

Liang Bai; Zihui Liu

doi:10.1007/s10623-019-00614-z

On the third greedy weight of 4-dimensional codes

Liang Bai, Zihui Liu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

1 Citation (Scopus)

Abstract

The upper bounds on the difference between the third greedy weight and the third generalized Hamming weight of 4-dimensional q-ary codes are obtained by using the finite geometry method. The codes achieving the upper bounds are constructed, and these codes are optimal with respect to the security when they are used in the wire-tap channel of type II with the coset coding scheme.

Original language	English
Pages (from-to)	2213-2230
Number of pages	18
Journal	Designs, Codes, and Cryptography
Volume	87
Issue number	10
DOIs	https://doi.org/10.1007/s10623-019-00614-z
Publication status	Published - 1 Oct 2019

Keywords

Finite geometry method
Generalized Hamming weight
Greedy weight
Wire-tap channel

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10.1007/s10623-019-00614-z

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title = "On the third greedy weight of 4-dimensional codes",

abstract = "The upper bounds on the difference between the third greedy weight and the third generalized Hamming weight of 4-dimensional q-ary codes are obtained by using the finite geometry method. The codes achieving the upper bounds are constructed, and these codes are optimal with respect to the security when they are used in the wire-tap channel of type II with the coset coding scheme.",

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AB - The upper bounds on the difference between the third greedy weight and the third generalized Hamming weight of 4-dimensional q-ary codes are obtained by using the finite geometry method. The codes achieving the upper bounds are constructed, and these codes are optimal with respect to the security when they are used in the wire-tap channel of type II with the coset coding scheme.

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KW - Generalized Hamming weight

KW - Greedy weight

KW - Wire-tap channel

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On the third greedy weight of 4-dimensional codes

Abstract

Keywords

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