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 Fpm + uFpm are considered, where p is a prime and m > 0 is any integer. The b-symbol distance for prime power length, i.e. ps 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 Fpm + uFpm which is of the form ζ and φ + uφ, where 0 ≠ 6 φ, φ, ζ ∈ Fpm. 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 ps over Fpm + uFpm are established.

Keywords

• Constacyclic codes
• repeated-root
• MDS codes
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