<p>BCH codes are a special kind of cyclic codes, which have important applications in the field of communication. There are many interesting problems with BCH codes. In this paper, we determine explicit minimum distance for BCH codes under certain conditions. Further, we construct quantum synchronizable codes using BCH codes over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_815_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mathbb {F}_q \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation> of length <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_815_Article_IEq2.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\( \frac{q^m-1}{a} \)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mrow> <msup> <mi>q</mi> <mi>m</mi> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mi>a</mi> </mfrac> </math></EquationSource> </InlineEquation> with explicit minimum distance. As a special class of quantum error-correcting codes, quantum synchronizable codes can not only correct quantum phase errors and bit errors, but also have synchronization recovery capability. Our construction ensures that these quantum synchronizable codes tolerate maximum number of misalignment errors.</p>