Minimal linear codes from characteristic functions

Minimal linear codes from characteristic functions

Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of \(\mathbb{F}_q\) to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary...

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Veröffentlicht in:arXiv.org 2019-11
Hauptverfasser: Mesnager, Sihem, Qi, Yanfeng, Ru, Hongming, Tang, Chunming
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Binary codes
Characteristic functions
Codes
Linear codes
Subspaces
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description Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of \(\mathbb{F}_q\) to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of \(\mathbb{F}_q\), we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes.
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subjects Binary codes
Characteristic functions
Codes
Linear codes
Subspaces
title Minimal linear codes from characteristic functions
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