BCH codes are important error correction codes, widely utilized due to their robust algebraic structure, multierror correcting capability, and efficient decoding algorithms. Despite their practical importance and extensive study, their parameters, including dimension, minimum distance and Bose distance, remain largely unknown in general. This paper addresses this challenge by investigating the dimension and Bose distance of BCH codes of length (qm−1)/λ over the finite field Fq, where λ is a positive divisor ofq−1. Specifically, for narrowsense BCH codes of this length withm≥ 4, we derive explicit formulas for their dimension for designed distances 2 ≤ δ ≤ (q⌊(2m−1)/3⌋+1−1)/λ+1. We also provide explicit formulas for their Bose distance in the range 2 ≤ δ ≤ (q⌊(2m−1)/3⌋+1 − 1)/λ. These ranges for δ are notably larger than the previously known results for this class of BCH codes. Furthermore, we extend these findings to determine the dimension and Bose distance for certain non-narrow-sense BCH codes of the same length. Several optimal linear codes can be obtained from these BCH codes.

Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes are a significant class of cyclic codes that play an important role in both theoretical research and practical applications. Their strong error-correcting abilities and efficient encoding and decoding methods make BCH codes widely applicable in various areas, including communication systems, data storage devices, and consumer electronics. Although BCH codes have been extensively studied, the parameters of BCH codes are not known in general. Letqbe a prime power andmbe a positive integer. Denote byC(q,m,δ))the narrow-sense primitive BCH code with lengthqm− 1 and designed distance δ. As of now, the dimensions ofC(q,m,δ)are fully understood only form≤ 2. Form≥ 4, the dimensions ofC(q,m,δ)are known only for the range 2 ≤ δ ≤q⌊(m+1)/2⌋+1and for a limited number of special cases. In this paper, we determined the dimension and Bose distance ofC(q,m,δ)form≥ 4 and δ ∈ [2,q⌊(2m−1)/3⌋+1]. Additionally, we have also extended our results to primitive BCH codes that are not necessarily narrow-sense.