Galois Self-Dual 2-Quasi Constacyclic Codes Over Finite Fields

Let F be a field with cardinality p(l) and 0 not equal lambda is an element of F, and 0 <= h < l. Extending Euclidean and Hermitian inner products, Fan and Zhang introduced Galois p(h)-inner product (DCC, vol.84, pp.473-492). In this paper, we characterize the structure of 2-quasi lambda-constacyclic codes over F; and exhibit necessary and sufficient conditions for 2-quasi lambda-constacyclic codes being Galois ph-self-dual. With the help of a technique developed in this paper, we prove that, when l is even, the Hermitian selfdual 2-quasi lambda-constacyclic codes are asymptotically good if and only if lambda(1+pl/2) = 1. And, when p(l) not equivalent to 3 (mod 4), the Euclidean self-dual 2-quasi lambda-constacyclic codes are asymptotically good if and only if lambda(2) = 1.