Bounds on MLDR Codes Over \mathbb Z_p^t

2024/08/20 by T. L. Alderson, Alderson, Tim L.
Computer Science · Engineering · #94B65 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2408.11107

openalex publication_date 2024/08/20 · openalex created_date 2024/12/16 · openalex updated_date 2026/07/28

Abstract

Upper bounds on the minimum Lee distance of codes that are linear over \mathbb Z_q, q=p^t, p prime are discussed. The bounds are Singleton like, depending on the length, rank, and alphabet size of the code. Codes meeting such bounds are referred to as Maximum Lee Distance with respect to Rank (MLDR) Codes. We present some new bounds on MLDR codes, using combinatorial arguments. In the context of MLDR codes, our work provides improvements over existing bounds in the literature

Related

• On the Linear Programming Bound for Lee-codes
• Better bounds on the minimal Lee distance
• On Codes Over ℤ_p^s with the Extended Lee Weight
• Lower bounds on the minimum distance of long codes in the Lee metric
• New LMRD bounds for constant dimension codes and improved constructions