New Galois hulls of generalized Reed-Solomon codes

作者：Wu, Yansheng; Li, Chengju; Yang, Shangdong^*

来源：Finite Fields and their Applications, 2022, 83: 102084.

DOI：10.1016/j.ffa.2022.102084

• Generalized Reed-Solomon code
• Galois hull
• Goppa code

Most recently, Gao et al. found a nice method to investigate the Euclidean hulls of generalized Reed-Solomon codes in terms of Goppa codes. In this note, we extend the results to general Galois hull. We prove that the Galois hulls of some GRS codes are still GRS codes. We also give some examples on Galois LCD and self-dual MDS codes. Compare with known results, the Galois hulls of GRS codes obtained in this work have flexible parameters.

• 单位
  西安电子科技大学; 南京邮电大学