On the symbol-pair distance of some classes of repeated-root constacyclic codes over Galois ring

Abstract

Let γ= 4 z- 1 be an unit of Type (∗ -) of the Galois ring GR(2a,m). The γ-constacyclic codes of length 2 s over the Galois ring GR(2a,m) are precisely the ideals ⟨ (x+ 1) i⟩ , 0 ≤ i≤ 2 sa of the chain ring R(a,m,γ)=GR(2a,m)[x]⟨x2s-γ⟩. This structure is used to determine the symbol pair distance of γ-constacyclic codes of length 2 s over GR(2a,m). The exact symbol-pair distances for all such γ-constacyclic codes of length 2 s over GR(2a,m) are obtained. Also, we provide the MDS symbol-pair codes of length 2 s over GR(2a,m) and some examples are computed.