Enhancing echelon-ferrers construction for constant dimension code

Echelon-Ferrers construction is one of the most powerful methods to improve the lower bounds for constant dimension codes. Although the method was proposed more than 10 years ago, it is still the best construction in a number of cases. In this paper, we remove parts of lifted FDRM codes from the echelon-Ferrers construction, and insert an SC-representation set, which finally improves the Echelon-ferrers construction, to get lower bounds for the following cases: A_q(11,4,4), A_q(15,4,4) and A_q(19,4,4) .