The b-symbol weight distribution of irreducible cyclic codes and related consequences

2022/03/22 by Hongwei Zhu, Zhu, Hongwei, Minjia Shi +1
Computer Science · #05 E30 #94 B15 #94 B25 #Cellular Automata and Applications #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2203.11567

openalex publication_date 2022/03/22 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

The b-symbol read channel is motivated by the limitations of the reading process in high density data storage systems. The corresponding new metric is a generalization of the Hamming metric known as the b-symbol weight metric and has become an important object in coding theory. In this paper, the general b-symbol weight enumerator formula for irreducible cyclic codes is presented by using the Gaussian period and a new invariant #U(b,j,N₁). The related b-symbol weight hierarchies \d₁(\C),d₂(\C),…,d_K(\C)\ (K=dim(\C)) are given for some cases. The shortened codes which are optimal from some classes of irreducible cyclic codes are given, where the shorten set T is the complementary set of b-symbol support of some codeword with the minimal b-symbol weight.

Related

• Complete b-symbol weight distribution of some irreducible cyclic codes
• The b-symbol weight distributions of all semiprimitive irreducible cyclic codes
• Two classes of reducible cyclic codes with large minimum symbol-pair distances
• Some bounds on the cardinality of the b-symbol weight spectrum of codes
• The weight Enumerator of some irreducible cyclic codes