MDS self-dual codes of lengths 16 and 18 (Q622784)

Summary: We demonstrate that an MDS self-dual [16, 8, 9] code over double struck capital \(\mathbb F_{p}\) exists for an odd prime number \(p\) with \(23 \leq p \leq 499\) 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 \(\mathbb F_{p}\) are also constructed for \(p = 53, 61, 73, 89, 97\).