Constructing MDS Galois self-dual constacyclic codes over finite fields

Abstract

As a further development and deepening of two examples in the paper (Fan and Zhang, 2017), we construct MDS Galois self-dual constacyclic codes over finite fields. First, we give the definition of normal MDS constacyclic codes and explore their existence conditions. Further, we give existence conditions for normal MDS Galois self-dual constacyclic codes. Based on the latter conditions, we classify and construct all normal MDS Galois self-dual λ-constacyclic codes over Fq of length n, where q=pe is an odd prime power, gcd(q,n)=1 and λ∈Fq∗.