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Erschienen in:
04.11.2021
Some t-designs from BCH codes
Erschienen in: Cryptography and Communications | Ausgabe 3/2022
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Abstract
Combinatorial t-designs are closely related to coding theory and finite geometries and have nice applications in some engineering areas. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. In this paper, this approach is further investigated with a class of linear codes related to the extended BCH codes and their duals over finite fields. By determining the parameters of these codes, an infinite family of 3-designs is presented and their parameters are also explicitly determined. In addition, the parameters of some combinatorial 2-designs from the extended codes of certain primitive BCH codes are also determined. Moreover, Research Problem 9.4 proposed by Ding in [Designs from Linear Codes, World Scientific, Singapore, pp: 257, 2018)] is also solved.