MDS self-dual codes of lengths 16 and 18

Abstract

We demonstrate that an MDS self-dual [16, 8, 9] code over double struck capital F p exists for an odd prime number p with 23 ≤ p ≤ 499 by constructing new MDS self-dual codes for the open cases. These codes are obtained using two construction methods based on negacirculant matrices. MDS self-dual [18, 9, 10] codes over double struck capital F p are also constructed for p = 53, 61, 73, 89, 97.