A Hierarchical-based Greedy Algorithm for Echelon-Ferrers Construction
Xianmang He · arXiv (Cornell University) · 2019
Echelon-Ferrers is one of important techniques to help researchers to improve lower bounds for subspace code. But, unfortunately, heavy computation has been paid as the cost for the construction. In this paper, we show how to attain codes of larger size for a given minimum distance d by the greedy algorithm for echelon-Ferrers construction introduced in [1]. This algorithm allows us to improve the lower bounds for several types of constant-dimension subspace codes, including Aq(15; 6; 6), Aq(16; 6; 6), and Aq(16; 6; 7) etc. More than 56 new improvements and the expression of these bounds are given. All these bounds exceeds the current best bounds.