期刊
DESIGNS CODES AND CRYPTOGRAPHY
卷 89, 期 5, 页码 823-841出版社
SPRINGER
DOI: 10.1007/s10623-021-00847-x
关键词
Self-orthogonal code; Self-dual code; MDS code; Almost MDS code; Optimal code; Algebraic curve; Algebraic geometry code; Differential algebraic geometry code
资金
- Anhui Provincial Natural Science Foundation [1908085MA04]
The author has constructed families of MDS Euclidean self-dual codes from genus zero algebraic geometry (AG) codes and explored more families of optimal Euclidean self-dual codes from AG codes. New families of MDS Euclidean self-dual codes of odd characteristic and almost MDS Euclidean self-dual codes are explicitly constructed from genus zero and genus one curves, respectively. Additional families of Euclidean self-dual codes are constructed from algebraic curves of higher genus.
Recently, the author has constructed families of MDS Euclidean self-dual codes from genus zero algebraic geometry (AG) codes. In the present correspondence, more families of optimal Euclidean self-dual codes from AG codes are explored. New families of MDS Euclidean self-dual codes of odd characteristic and those of almost MDS Euclidean self-dual codes are constructed explicitly from genus zero and genus one curves, respectively. More families of Euclidean self-dual codes are constructed from algebraic curves of higher genus.
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