On self-dual constacyclic codes over finite fields

Self-dual and self-orthogonal negacyclic codes of length2mpnover a finite field

“…This characterization provides simple conditions on the existence of self-dual negacyclic codes and generalizes the work of Dinh [11]. Yang and Cai [21] derived necessary and sufficient conditions for the existence of Hermitian self-dual codes of length n over F q 2 .…”

Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields

“…, c n−2 ) is again a codeword in C. A λ-constacyclic code is called cyclic and negacyclic if λ = 1 and λ = −1, respectively. It is well known (see, for example, [29]) that every λ-constacyclic code C of length n over F q 2 can be identified with an ideal in F q 2 [x]/ x n − λ generated by a unique monic divisor of x n − λ. Such a polynomial is called the generator polynomial of C.…”

“…Let g(x) be the generator polynomial of a λ-constacyclic code C of length n over F q 2 and let h(x) = x n −λ g (x) . Then h † (x) is a monic divisor of x n − λ and it is the generator polynomial of C ⊥ H (see [29,Lemma 2.1]). Therefore, C is Hermitian self-dual if and only if g(x) = h † (x).…”

“…For a nonzero λ ∈ F q 2 , let o q 2 (λ) denote the order of λ in the multiplicative group F × q 2 := F q 2 {0}. In [29,Proposition 2.3], it has been shown that the Hermitian dual of a λ-constacyclic code is also λ-constacyclic if and only if o q 2 (λ)|(q+1). Later, in Proposition 6.2, we show that the Hermitian dual of a (λ, ℓ)-QT code over F q 2 is again (λ, ℓ)-QT if and only if o q 2 (λ)|(q + 1).…”

New MDS Euclidean and Hermitian Self-Dual Codes over Finite Fields

“…There are many papers discussing Hermitian self-dual codes. [7] [16][18] [20] If C is MDS and Euclidean self-dual or Hermitian self-dual, C is called an MDS Euclidean self-dual code or an MDS Hermitian self-dual code, respectively. In recent years, study of MDS self-dual codes has attracted a lot of attention.…”