Non-free extensions of the simplex codes over a chain ring with four elements
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- 作者：Thomas Honold (1)
Ivan Landjev (2) - 关键词：Simplex code ; Chain ring ; Projective Hjelmslev space ; Hjelmslev plane ; Hyperoval ; Lee weight ; R ; linear code ; Gray map ; 94B05 ; 94B27 ; 51C05 ; 51E21 ; 51E26
- 刊名：Designs, Codes and Cryptography
- 出版年：2013
- 出版时间：3 - January 2013
- 年：2013
- 卷：66
- 期：1
- 页码：27-38
- 全文大小：192KB
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20. Landjev I., Honold T.: Arcs in projective Hjelmslev planes. Discret. Math. Appl. 11(1), 53鈥?0 (2001). Originally published in Diskretnaya Matematika 131, 90鈥?09 (2001) (in Russian). - 作者单位：Thomas Honold (1)
Ivan Landjev (2)
1. Department of Information Science and Electronics Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, China
2. New Bulgarian University, 21 Montevideo Str., 1618, Sofia, Bulgaria - ISSN：1573-7586
文摘
Let R be a chain ring with four elements. In this paper, we present two new constructions of R-linear codes that contain a subcode associated with a simplex code over the ring R. The simplex codes are defined as the codes generated by a matrix having as columns the homogeneous coordinates of all points in some projective Hjelmslev geometry PHG(R k ). The first construction generalizes a recent result by Kiermaier and Zwanzger to codes of arbitrary dimension. We provide a geometric interpretation of their construction which is then extended to projective Hjelmslev spaces of arbitrary dimension. The second construction exploits the possibility of adding two non-free rows to the generator matrix of a linear code over R associated with a given point set. Though the construction works over both chain rings with four elements, the better codes are obtained for ${R=\mathbb{Z}_4}$ .