廖崟琎, 何佳维. 三类基于Weil sums的线性码[J]. 南昌航空大学学报(自然科学版), 2025, 39(2): 35-42. DOI: 10.3969/j.issn.2096-8566.2025.02.005
引用本文: 廖崟琎, 何佳维. 三类基于Weil sums的线性码[J]. 南昌航空大学学报(自然科学版), 2025, 39(2): 35-42. DOI: 10.3969/j.issn.2096-8566.2025.02.005
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Yinjin LIAO, Jiawei HE. Three Classes of Linear Codes Based on Weil Sums[J]. Journal of nanchang hangkong university(Natural science edition), 2025, 39(2): 35-42. DOI: 10.3969/j.issn.2096-8566.2025.02.005
Citation: Yinjin LIAO, Jiawei HE. Three Classes of Linear Codes Based on Weil Sums[J]. Journal of nanchang hangkong university(Natural science edition), 2025, 39(2): 35-42. DOI: 10.3969/j.issn.2096-8566.2025.02.005
shu

三类基于Weil sums的线性码

Three Classes of Linear Codes Based on Weil Sums

    摘要
  • 摘要: 近年来，少重量线性码被广泛地研究。少重量线性码在强正则图、密钥分享方案、关联方案以及认证码等领域均有应用。本文选取特定定义集，进而构造出有限域上的三类6-重量线性码，并借助Weil sums确定这三类线性码的重量分布情况。

     

    Abstract: In recent years, linear codes with few weights have been extensively studied. Linear codes with few weights are applied in such fields as strongly regular graphs, secret sharing schemes, association schemes and authentication codes. In this paper, a specific defining set is first selected. Based on this, three classes of 6-weight linear codes over finite fields are constructed. Finally, their weight distributions are characterized by using Weil sums.

     

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