Abstract
In Wu (Linear Algebra Appl 439:422---434 2013), the author constructed a binary code using the incidence matrix of conics consisting only of internal points with respect to a fixed conic versus internal points and studied geometric problems associated with this code. Inspired by that work, in this article, we construct conics consisting only of external points with respect to a conic for $$q$$q odd. We study the intersection pattern of each of these conics with secant lines of the fixed conic, compute the dimension of the $${\mathbb F}_2$$F2-row space of the incidence matrix of the aforementioned conics and external points which provides us with the dimension of the associated binary code, and find the automorphism group of the binary code.
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