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On the parameters of extended primitive cyclic codes and the related designs.
- Source :
- Designs, Codes & Cryptography; Jun2024, Vol. 92 Issue 6, p1533-1540, 8p
- Publication Year :
- 2024
-
Abstract
- Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight in this code support a 2-design. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined and the parameters of the related 2-designs are also given. Moreover, we prove that the minimum weight codewords in this code support a 3-design when p = 2 , which gives an affirmative answer to Heng's conjecture. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09251022
- Volume :
- 92
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Designs, Codes & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 177310003
- Full Text :
- https://doi.org/10.1007/s10623-024-01357-2