Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes

2020/10/06 by Boran Kim, Kim, Boran
Computer Science · Engineering · Mathematics · #94B15 #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT #msc:94B15

paper · pdf · doi:10.48550/arxiv.2010.02471

openalex publication_date 2020/10/06 · arxiv created 2021/10/18 · arxiv updated 2021/10/19 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom-Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over \mathfrak R=\Bbb F_p^m[u]/⟨ u⁴⟩ of length n=p^k. For the determination, we explicitly present third torsional degree for all different types of cyclic codes over \mathfrak R of length n.

Related

• The symbol-pair distance distribution of repeated-root cyclic codes over \mathbbF_p^m
• Two classes of reducible cyclic codes with large minimum symbol-pair distances
• b-symbol distance distribution of repeated-root cyclic codes
• AMDS Symbol-Pair Codes from Repeated-Root Cyclic Codes
• The b-symbol weight distribution of irreducible cyclic codes and related consequences