On the nonexistence of triple-error-correcting perfect binary linear codes with a crown poset structure

摘要

Ahn et al. [Discrete Math. 268 (2003) 21–30] characterized completely the parameters of single- and error-correcting perfect linear codes with a crown poset structure by solving Ramanujan–Nagell-type Diophantine equation. In this paper, we give a shorter proof for the same result by analyzing a generator matrix of a perfect linear code. Furthermore, we combine our method with the Johnson bound in coding theory to prove that there are no triple-error-correcting perfect binary codes with a crown poset structure.