Some 3-designs and shortened codes from binary cyclic codes with three zeros

2022/06/30 by Can Xiang, Chunming Tang, Xiang, Can +1 · 2 citations
Computer Science · Engineering · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #VLSI and Analog Circuit Testing #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2206.15153

openalex publication_date 2022/06/30 · openalex created_date 2022/07/03 · openalex updated_date 2026/07/28

Abstract

Linear codes and t-designs are interactive with each other. It is well known that some t-designs have been constructed by using certain linear codes in recent years. However, only a small number of infinite families of the extended codes of linear codes holding an infinite family of t-designs with t≥ 3 are reported in the literature. In this paper, we study the extended codes of the augmented codes of a class of binary cyclic codes with three zeros and their dual codes, and show that those codes hold 3-designs. Furthermore, we obtain some shortened codes from the studied cyclic codes and explicitly determine their parameters. Some of those shortened codes are optimal or almost optimal.

Cited by

• The extended code for a class of generalized Roth-Lempel codes and their properties
• Combinatorial t-Designs from Finite Abelian Groups and Their Applications to Elliptic Curve Codes

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