2022/10/21 by Atul Kumar Shriwastva, Shriwastva, Atul Kumar, R. S. Selvaraj +1
Computer Science · Engineering · Mathematics · #06A06 #15A03 #94B05 #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2210.12183
openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given [n]=\1,2,…,n\, a partial order \preceq on [n], a label map π: [n] → ℕ defined by π(i) = ki with ∑i=1nπ(i) = N, the direct sum \mathbbFqk1 ⊕ \mathbbFqk2⊕ … ⊕ \mathbbFqkn of \mathbbFqN , and a weight function w on \mathbbFq , we define a poset block metric d(P,w,π) on \mathbbFqN based on the poset P=([n],\preceq). The metric d(P,w,π) is said to be weighted coordinates poset block metric ((P,w,π)-metric). It extends the weighted coordinates poset metric ((P,w)-metric) introduced by L. Panek and J. A. Pinheiro and generalizes the poset block metric ((P,π)-metric) introduced by M. M. S. Alves et al. We determine the complete weight distribution of a (P,w,π)-space, thereby obtaining it for (P,w)-space, (P,π)-space, π-space, and P-space as special cases. We obtain the Singleton bound for (P,w,π)-codes and for (P,w)-codes as well. In particular, we re-obtain the Singleton bound for any code with respect to (P,π)-metric and P-metric. Moreover, packing radius and Singleton bound for NRT block codes are found.