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

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