b-Symbol Distance of Constacylic Codes of Length p^s Over F_p ^m + uF_p ^m

Abstract

In this research paper, the repeated-root constacyclic codes over the chain ring F p m + uF p m are considered, where p is a prime and m > 0 is any integer. The b-symbol distance for prime power length, i.e. p s is also studied for any integer s > 0. The Hamming and symbol-pair distances of all δ-constacyclic codes have been thoroughly studied in [18], where δ is an unit in the ring F p m + uF p m which is of the form ζ and φ + uϕ, where 0 = φ, ϕ, ζ ∈ F p m. In this paper, the b-symbol distance of all such δ-constacyclic codes of prime power length is computed for 1 ≤ b ≤ p 2. Furthermore, as an application, all MDS b-symbol constacyclic codes of length p s over F p m + uF p m are established. INDEX TERMS Constacyclic codes, repeated-root, MDS codes, b-symbol distance.