Some sufficient conditions for <inline-formula><tex-math id="M1">$ (\mathcal{A*B})^\perp $</tex-math></inline-formula> with an error-correcting pair <inline-formula><tex-math id="M2">$ (\mathcal{A},\mathcal{B}) $&l

As a general algebraic decoding method for linear codes, the $ t $-error-correcting pair can correct up to $ t $ errors in polynomial times. Based on two fixed linear codes $ \mathcal{A} $ and $ \mathcal{B} $, we gave some sufficient conditions such that $ (\mathcal{A*B})^\perp $ is either an MDS or AMDS linear code, and $ (\mathcal{A}, \mathcal{B}) $ is a $ t $-error-correcting pair for $ (\mathcal{A*B})^\perp $. Furthermore, some corresponding examples were given based on TGRS codes.