Linear codes with a few-weight have important applications in combinatorial design, strongly regular graphs and cryptography. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra, and determine their spectrum distribution. Then, we derive two classes of linear codes with at most six-weight from the new functions. Meanwhile, the length, dimension and weight distributions of the codes are obtained. Results show that both of the new codes are minimal and among them, one is wide minimal code and the other is a narrow minimal code and thus can be used to design secret sharing scheme with good access structures. Finally, some Magma programs are used to verify the correctness of our results.
Jiawei DU
Northwest Normal University,Guilin University of Electronic Technology
Xiaoni DU
Northwest Normal University
Wengang JIN
Northwest Normal University
Yingzhong ZHANG
Northwest Normal University
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Jiawei DU, Xiaoni DU, Wengang JIN, Yingzhong ZHANG, "Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 4, pp. 689-693, April 2022, doi: 10.1587/transfun.2021EAP1062.
Abstract: Linear codes with a few-weight have important applications in combinatorial design, strongly regular graphs and cryptography. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra, and determine their spectrum distribution. Then, we derive two classes of linear codes with at most six-weight from the new functions. Meanwhile, the length, dimension and weight distributions of the codes are obtained. Results show that both of the new codes are minimal and among them, one is wide minimal code and the other is a narrow minimal code and thus can be used to design secret sharing scheme with good access structures. Finally, some Magma programs are used to verify the correctness of our results.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1062/_p
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@ARTICLE{e105-a_4_689,
author={Jiawei DU, Xiaoni DU, Wengang JIN, Yingzhong ZHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function},
year={2022},
volume={E105-A},
number={4},
pages={689-693},
abstract={Linear codes with a few-weight have important applications in combinatorial design, strongly regular graphs and cryptography. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra, and determine their spectrum distribution. Then, we derive two classes of linear codes with at most six-weight from the new functions. Meanwhile, the length, dimension and weight distributions of the codes are obtained. Results show that both of the new codes are minimal and among them, one is wide minimal code and the other is a narrow minimal code and thus can be used to design secret sharing scheme with good access structures. Finally, some Magma programs are used to verify the correctness of our results.},
keywords={},
doi={10.1587/transfun.2021EAP1062},
ISSN={1745-1337},
month={April},}
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TY - JOUR
TI - Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 689
EP - 693
AU - Jiawei DU
AU - Xiaoni DU
AU - Wengang JIN
AU - Yingzhong ZHANG
PY - 2022
DO - 10.1587/transfun.2021EAP1062
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2022
AB - Linear codes with a few-weight have important applications in combinatorial design, strongly regular graphs and cryptography. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra, and determine their spectrum distribution. Then, we derive two classes of linear codes with at most six-weight from the new functions. Meanwhile, the length, dimension and weight distributions of the codes are obtained. Results show that both of the new codes are minimal and among them, one is wide minimal code and the other is a narrow minimal code and thus can be used to design secret sharing scheme with good access structures. Finally, some Magma programs are used to verify the correctness of our results.
ER -