Construction of Two Classes of Minimal Binary Linear Codes

DU Xiaoni; HU Jinxia; JIN Wengang; SUN Yanzhong

doi:10.11999/JEIT210720

Volume 44 Issue 10

Oct. 2022

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2022 > 44(10): 3643-3649

Jiang Yu-Wen, Tan Le-Yi, Wang Shou-Jue. Saliency Detected Model Based on Selective Edges Prior[J]. Journal of Electronics & Information Technology, 2015, 37(1): 130-136. doi: 10.11999/JEIT140119

Citation:

DU Xiaoni, HU Jinxia, JIN Wengang, SUN Yanzhong. Construction of Two Classes of Minimal Binary Linear Codes[J]. Journal of Electronics & Information Technology, 2022, 44(10): 3643-3649. doi: 10.11999/JEIT210720

Jiang Yu-Wen, Tan Le-Yi, Wang Shou-Jue. Saliency Detected Model Based on Selective Edges Prior[J]. Journal of Electronics & Information Technology, 2015, 37(1): 130-136. doi: 10.11999/JEIT140119

Citation:

PDF( 581 KB)

Construction of Two Classes of Minimal Binary Linear Codes

doi: 10.11999/JEIT210720

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Funds: The National Natural Science Foundation of China (61772022, 62172337)

Received Date: 2021-07-16
Rev Recd Date: 2022-04-03

Available Online: 2022-04-22

Publish Date: 2022-10-19

Abstract

Abstract

Linear codes play an important role in data storage, information security and secret sharing. Minimal linear codes are the first choice to design secret sharing schemes, so the design of minimal linear codes is one of the important contents of current cryptosystem and coding theory. In this paper, the Walsh spectrum distribution of the selected Boolean functions is studied, and two kinds of minimal linear codes are obtained by using the Walsh spectrum distribution of the functions, then the weight distribution of the codes are determined. The results show that the constructed codes are minimal linear codes that do not satisfy the Ashikhmin-Barg condition, and can be used to design secret sharing schemes with good access structure.
- Boolean functions,
- Walsh transform,
- Binary linear codes

FullText(HTML)

References(16)

References

[1]	ÇALKAVUR S. A study on multisecret-sharing schemes based on linear codes[J]. Emerging Science Journal, 2020, 4(4): 263–271. doi: 10.28991/esj-2020-01229
[2]	WANG Yaru, LI Fulin, and ZHU Shixin. Two-weight linear codes and their applications in secret sharing[J]. Chinese Journal of Electronics, 2019, 28(4): 706–711. doi: 10.1049/cje.2019.04.006
[3]	CHABANNE H, COHEN G, and PATEY A. Towards secure two-party computation from the wire-tap channel[C]. The 16th International Conference on Information Security and Cryptology, Seoul, Korea, 2014: 34–46.
[4]	NIEMINEN R and JÄRVINEN K. Practical privacy-preserving indoor localization based on secure two-party computation[J]. IEEE Transactions on Mobile Computing, 2021, 20(9): 2877–2890. doi: 10.1109/TMC.2020.2990871
[5]	WANG Qichun and STĂNICĂ P. New bounds on the covering radius of the second order Reed-Muller code of length 128[J]. Cryptography and Communications, 2019, 11(2): 269–277. doi: 10.1007/s12095-018-0289-2
[6]	CARLET C. The automorphism groups of the Kerdock codes[J]. Journal of Information and Optimization Sciences, 1991, 12(3): 387–400. doi: 10.1080/02522667.1991.10699078
[7]	BAUMERT L D and MCELIECE R J. Weights of irreducible cyclic codes[J]. Information and Control, 1972, 20(2): 158–175. doi: 10.1016/S0019-9958(72)90354-3
[8]	DING Cunsheng and NIEDERREITER H. Cyclotomic linear codes of order 3[J]. IEEE Transactions on Information Theory, 2007, 53(6): 2274–2277. doi: 10.1109/TIT.2007.896886
[9]	XIANG Can. Linear codes from a generic construction[J]. Cryptography and Communications, 2016, 8(4): 525–539. doi: 10.1007/s12095-015-0158-1
[10]	DING Cunsheng. A construction of binary linear codes from Boolean functions[J]. Discrete Mathematics, 2016, 339(15): 2288–2303. doi: 10.1016/j.disc.2016.03.029
[11]	CHANG S and HYUN J Y. Linear codes from simplicial complexes[J]. Designs, Codes and Cryptography, 2018, 86(10): 2167–2181. doi: 10.1007/s10623-017-0442-5
[12]	HENG Ziling, DING Cunsheng, and ZHOU Zhengchun. Minimal linear codes over finite fields[J]. Finite Fields and Their Applications, 2018, 54: 176–196. doi: 10.1016/j.ffa.2018.08.010
[13]	DING Cunsheng, HENG Ziling, and ZHOU Zhengchun. Minimal binary linear codes[J]. IEEE Transactions on Information Theory, 2018, 64(10): 6536–6545. doi: 10.1109/TIT.2018.2819196
[14]	MESNAGER S, QI Yanfeng, RU Hongming, et al. Minimal linear codes from characteristic functions[J]. IEEE Transactions on Information Theory, 2020, 66(9): 5404–5413. doi: 10.1109/TIT.2020.2978387
[15]	ASHIKHMIN A and BARG A. Minimal vectors in linear codes[J]. IEEE Transactions on Information Theory, 1998, 44(5): 2010–2017. doi: 10.1109/18.705584
[16]	MACWILLIAMS F J and SLOANE N J A. The Theory of Error-Correcting Codes[M]. Amsterdam: Elsevier-North-Holland, 1997.

Relative Articles

Supplements(0)

Cited By

Cited by

Periodical cited type(20)

1.	周晨，周乾伟，陈翰墨，管秋，胡海根，吴延壮. 面向RGBD图像显著性检测的循环逐尺度融合网络. 小型微型计算机系统. 2023(10): 2276-2283 .
2.	叶海峰，赵玉琛. 视觉位置识别中代表地点的标识牌算法. 小型微型计算机系统. 2021(04): 823-828 .
3.	王慧玲，宋鑫怡，杨颖. 基于优化查询的改进显著性检测算法. 吉林大学学报(信息科学版). 2020(03): 319-324 .
4.	郭迎春，李卓. 基于边缘特征和自适应融合的视频显著性检测. 河北工业大学学报. 2019(01): 1-7 .
5.	鲁文超，段先华，徐丹，王万耀. 基于多尺度下凸包改进的贝叶斯模型显著性检测算法. 计算机科学. 2019(06): 295-300 .
6.	王宝艳，张铁，李凯，杜松林. DEL分割算法对SSLS算法的改进. 小型微型计算机系统. 2019(10): 2052-2057 .
7.	张巧荣，徐国愚，张俊峰. 利用视觉显著性的前景目标分割. 兰州大学学报(自然科学版). 2019(06): 833-840 .
8.	杨俊丰，林亚平，欧博，蒋军强，李强. 基于显著性加权随机优化的快速响应码美化方法. 电子与信息学报. 2018(02): 289-297 . 本站查看
9.	邓晨，谢林柏. 全局对比和背景先验驱动的显著目标检测. 计算机工程与应用. 2018(03): 212-216 .
10.	刘亚宁，吴清，魏雪. 基于流行排序的前景背景显著性检测算法. 科学技术与工程. 2018(18): 74-81 .
11.	闫钧华，肖勇旗，姜惠华，杨勇，张寅. 融合区域像素显著性和时域信息的地面动目标检测及其DSP实现. 电子设计工程. 2018(19): 178-183+193 .
12.	陈厚仁，蔡延光. 基于视频的干线交通流检测系统的研究与实现. 工业控制计算机. 2017(07): 85-87 .
13.	赵艳艳，沈西挺. 基于同步更新的背景检测显著性优化. 计算机工程. 2017(10): 264-267 .
14.	田畅，姜青竹，吴泽民，刘涛，胡磊. 基于区域协方差的视频显著度局部空时优化模型. 电子与信息学报. 2016(07): 1586-1593 . 本站查看
15.	罗会兰，万成涛，孔繁胜. 基于KL散度及多尺度融合的显著性区域检测算法. 电子与信息学报. 2016(07): 1594-1601 . 本站查看
16.	张晴，林家骏，戴蒙. 基于图的流行排序的显著目标检测改进算法. 计算机工程与应用. 2016(22): 26-32+38 .
17.	杜永强. 过度曝光图像缺失信息修复算法. 科技通报. 2016(08): 146-149 .
18.	郎波，樊一娜，黄静. 利用混合高斯进行物体成分拟合匹配的算法. 科学技术与工程. 2016(20): 73-80 .
19.	项导，侯赛辉，王子磊. 基于背景学习的显著物体检测. 中国图象图形学报. 2016(12): 1634-1643 .
20.	吕建勇，唐振民. 一种基于图的流形排序的显著性目标检测改进方法. 电子与信息学报. 2015(11): 2555-2563 . 本站查看