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The minimum distance of new generalisations of the punctured binary Reed-Muller codes. (English) Zbl 1446.94193
Summary: In 2018, C. Ding et al. [Finite Fields Appl. 53, 144–174 (2018; Zbl 1393.94928)] introduced a new generalization of the punctured binary Reed-Muller codes to construct LCD codes and 2-designs. They studied the minimum distance of the codes and proposed an open problem about the minimum distance. In this paper, several new results on the minimum distance of the generalized punctured binary Reed-Muller are presented. Particularly, some of the results are a generalization or improvement of previous results in the paper cited above.
##### MSC:
 94B15 Cyclic codes 94B05 Linear codes (general theory) 94B65 Bounds on codes
##### Keywords:
Reed-Muller code; generalized Reed-Muller code; cyclic code
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##### References:
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