Abstract
BCH codes form a special subclass of cyclic codes and have been extensively studied in the past decades. Determining the parameters of BCH codes, however, has been an important but difficult problem. Recently, in order to further investigate the dual codes of BCH codes, the concept of dually-BCH codes was proposed. In this paper, we study BCH codes of lengths qm+1q+1 and qm+1 over the finite field Fq, both of which are LCD codes. The dimensions of narrow-sense BCH codes of length qm+1q+1 with designed distance δ=ℓqm−12+1 are determined, where q>2 and 2≤ℓ≤q−1. Lower bounds on the minimum distances of the dual codes of narrow-sense BCH codes of length qm+1 are developed for odd q, which are good in some cases. Moreover, sufficient and necessary conditions for the even-like subcodes of narrow-sense BCH codes of length qm+1 being dually-BCH codes are presented, where q is odd and m≢0(mod4).
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