Weight Distributions of Some Classes of Irreducible Quasi-cyclic Codes of Index 2

GAO Jian; ZHANG Yaozong; MENG Xiangrui; MA Fanghui

doi:10.11999/JEIT211104

Volume 44 Issue 12

Dec. 2022

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GAO Jian, ZHANG Yaozong, MENG Xiangrui, MA Fanghui. Weight Distributions of Some Classes of Irreducible Quasi-cyclic Codes of Index 2[J]. Journal of Electronics & Information Technology, 2022, 44(12): 4312-4318. doi: 10.11999/JEIT211104

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GAO Jian, ZHANG Yaozong, MENG Xiangrui, MA Fanghui. Weight Distributions of Some Classes of Irreducible Quasi-cyclic Codes of Index 2[J]. Journal of Electronics & Information Technology, 2022, 44(12): 4312-4318. doi: 10.11999/JEIT211104

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Weight Distributions of Some Classes of Irreducible Quasi-cyclic Codes of Index 2

doi: 10.11999/JEIT211104

School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China

Funds: The National Natural Science Foundation of China (12071264,11701336, 11626144, 11671235), The Natural Science Foundation of Shandong Province (ZR2021QA047), The IC Program of Shandong Institutions of Higher Learning For Youth Innovative Talents

Received Date: 2021-10-11
Accepted Date: 2022-05-05
Rev Recd Date: 2022-04-18

Available Online: 2022-05-07

Publish Date: 2022-12-16

Abstract

Abstract

Few-weight linear codes have important applications in constructing authentication codes, association schemes and secret sharing schemes. How to construct few-weight linear codes has always been an important topic of coding theory. In this paper, irreducible quasi-cyclic codes of index 2 over finite fields are constructed by selecting a special defining set. The weight distribution of several classes of irreducible quasi-cyclic codes of index 2 are determined by using Gaussian periods over finite fields. Some classes of 2-weight linear codes and 3-weight linear codes are obtained. The results show that two of the three classes of 2-weight linear codes constructed in this paper are Maximum Distance Separable (MDS) codes and the other class reaches Griesmer bound.
- Linear codes,
- Quasi-cyclic codes,
- Gaussian periods,
- Weight distributions

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References(19)

References

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