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 ≠ 6 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.
Highlights
The theory of error correcting codes attracted the attention of many researchers around the globe since its eruption
UFpm and b-distances of over Fpm of repeated root constacyclic codes of prime power lengths have been computed by Dinh et al [18], [19], recently
As all maximum distance separable (MDS) b-symbol constacyclic an application, we codes of length ps establish over the ring Fpm + uFpm
Summary
The theory of error correcting codes attracted the attention of many researchers around the globe since its eruption. Dinh et al.: b-Symbol Distance of Constacylic Codes of Length ps Over Fpm + uFpm. A Singleton Bound for b-symbol codes over Fq was established in [12] as follows: Let q be a prime power and b ≤. UFpm and b-distances of over Fpm of repeated root constacyclic codes of prime power lengths have been computed by Dinh et al [18], [19], recently. . As all MDS b-symbol constacyclic an application, we codes of length ps establish over the ring Fpm + uFpm. The organization of this paper is as follows. All the MDS b-symbol constacyclic codes of length ps are identified in Section 4 and in Section 5, we conclude the paper
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