b-Symbol Distance of Constacylic Codes of Length ps Over Fpm + uFpm

In this research paper, the repeated-root constacyclic codes over the chain ring <inline-formula> <tex-math notation="LaTeX">$\mathcal F_{p^{m}}+ u \mathcal F_{p^{m}}$ </tex-math></inline-formula> are considered, where <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> is a prime and <inline-formula> <tex-math notation="LaTeX">$m > 0$ </tex-math></inline-formula> is any integer. The <inline-formula> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>-symbol distance for prime power length, i.e. <inline-formula> <tex-math notation="LaTeX">$p^{\mathfrak {s}}$ </tex-math></inline-formula> is also studied for any integer <inline-formula> <tex-math notation="LaTeX">${\mathfrak {s}} > 0$ </tex-math></inline-formula>. The Hamming and symbol-pair distances of all <inline-formula> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula>-constacyclic codes have been thoroughly studied in <xref ref-type="bibr" rid="ref18">[18]</xref>, where <inline-formula> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> is an unit in the ring <inline-formula> <tex-math notation="LaTeX">$\mathcal F_{p^{m}}+ u \mathcal F_{p^{m}}$ </tex-math></inline-formula> which is of the form <inline-formula> <tex-math notation="LaTeX">$\zeta $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\phi + u \varphi $ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$0 \neq \phi, \varphi, \zeta \in \mathcal F_{p^{m}}$ </tex-math></inline-formula>. In this paper, the <inline-formula> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>-symbol distance of all such <inline-formula> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula>-constacyclic codes of prime power length is computed for <inline-formula> <tex-math notation="LaTeX">$1 \leq b \leq \lfloor \frac {p}{2}\rfloor $ </tex-math></inline-formula>. Furthermore, as an application, all MDS <inline-formula> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>-symbol constacyclic codes of length <inline-formula> <tex-math notation="LaTeX">$p^{\mathfrak {s}}$ </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">$\mathcal F_{p^{m}}+ u \mathcal F_{p^{m}}$ </tex-math></inline-formula> are established.