singular subspace
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2021 ◽  
Vol 49 (1) ◽  
pp. 370-392
Author(s):  
Zhigang Bao ◽  
Xiucai Ding ◽  
and Ke Wang

2019 ◽  
Vol 30 (05) ◽  
pp. 735-757
Author(s):  
Gang Wang ◽  
Min-Yao Niu ◽  
Fang-Wei Fu

In this paper, the Sphere-packing bound, Wang-Xing-Safavi-Naini bound, Johnson bound and Gilbert-Varshamov bound on the subspace code of length [Formula: see text], size [Formula: see text], minimum subspace distance [Formula: see text] based on [Formula: see text]-dimensional totally singular subspace in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over finite fields [Formula: see text] of characteristic 2, denoted by [Formula: see text], are presented, where [Formula: see text] is a positive integer, [Formula: see text], [Formula: see text], [Formula: see text]. Then, we prove that [Formula: see text] codes attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in [Formula: see text], where [Formula: see text] denotes the collection of all the [Formula: see text]-dimensional totally singular subspaces in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over [Formula: see text] of characteristic 2. Finally, Gilbert-Varshamov bound and linear programming bound on the subspace code [Formula: see text] in [Formula: see text] are provided, where [Formula: see text] denotes the collection of all the totally singular subspaces in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over [Formula: see text] of characteristic 2.


2017 ◽  
Vol 267 ◽  
pp. 201-209 ◽  
Author(s):  
Xiaowei Feng ◽  
Xiangyu Kong ◽  
Donghui Xu ◽  
Jianqiang Qin

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