On the Constructions of MDS Self-dual Codes via Cyclotomy

Abstract

MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and extended generalized Reed-Solomon codes as the candidates of MDS codes and taking their evaluation sets as an union of cyclotomic classes. The conditions on such MDS codes being self-dual are expressed in terms of cyclotomic numbers.

arXiv comment15 pages

References in corpus (1)

• Construction of MDS Self-dual Codes over Finite Fields

Cited by in corpus (3)

• A Note on Self-Dual Generalized Reed-Solomon Codes
• New constructions of MDS self-dual and self-orthogonal codes via GRS codes
• Construction of MDS Euclidean Self-Dual Codes via Two Subsets