Block Codes on Pomset Metric
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Given a regular multiset M on [n]={1,2,…,n}, a partial order R on M, and a label map π : [n] →ℕ defined by π(i) = k_i with ∑_i=1^nπ (i) = N, we define a pomset block metric d_(Pm,π) on the direct sum ℤ_m^k_1⊕ℤ_m^k_2⊕…⊕ℤ_m^k_n of ℤ_m^N based on the pomset ℙ=(M,R). This pomset block metric d_(Pm,π) extends the classical pomset metric which accommodate Lee metric introduced by I. G. Sudha and R. S. Selvaraj, in particular, and generalizes the poset block metric introduced by M. M. S. Alves et al, in general, over ℤ_m. We find I-perfect pomset block codes for both ideals with partial and full counts. Further, we determine the complete weight distribution for (P,π)-space, thereby obtaining it for (P,w)-space, and pomset space, over ℤ_m. For chain pomset, packing radius and Singleton type bound are established for block codes, and the relation of MDS codes with I-perfect codes is investigated. Moreover, we also determine the duality theorem of an MDS (P,π)-code when all the blocks have the same length.
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