Galois Self-dual 2-quasi Constacyclic Codes over Finite Fields · arXivDesk2404.08402Apr 12, 2024
Galois Self-dual 2-quasi Constacyclic Codes over Finite Fields
Yun Fan, Yue Leng
Abstract
Let F be a field with cardinality pℓ and 0=λ∈F, and 0≤h<ℓ
. Extending Euclidean and Hermitian inner products, Fan and Zhang introduced Galois
-inner product (DCC, vol.84, pp.473-492). In this paper, we characterize the structure of
-quasi
-constacyclic codes over
; and exhibit necessary and sufficient conditions for
-quasi
-constacyclic codes being Galois self-dual. With the help of a technique developed in this paper, we prove that, when
is even, the Hermitian self-dual
-quasi
-constacyclic codes are asymptotically good if and only if
λ1+pℓ/2=1 . And, when
pℓ≡3 (mod 4) , the Euclidean self-dual
-quasi
-constacyclic codes are asymptotically good if and only if
.