On the constructions of MDS self-dual codes via cyclotomy (Q2667085)

For an odd prime power \(q\), this paper studies the existence of an MDS-self dual code of even length over a finite field \(\mathbb{F}_q\). The authors use the well-known construction of MDS-self dual codes based on the generalized Reed-Solomon codes or extended generalized Reed-Solomon codes and taking their evaluation set as a union of cosets of any subgroup of multiplicative group \(\mathbb{F}_q^{*}\). For any subgroup of order \(f\) with \(q-1=ef\), these cosets are the \(e\)-th cyclotomic classes. Some applications are provided.