Chapter 5: On Hamming and $b$-symbol Distances of Constacyclic Codes of Length $ 4p^s$ over $ \Re$

Let $\mathbb{F}_{p^m}$ be the finite field of order $p^m$, where $p$ is an odd prime, and $m$ is a positive integers such that $p^m \equiv 1\pmod{4}$ holds. Here, we determine the Hamming and $b$-symbol distances for all $\Lambda$-constacyclic codes of length $4p^s$ over $\Re$ for any non-square unit $\Lambda$ and positive integer $s$, and use this distance distribution to provide several codes with new parameters. As an application, we identify all the MDS codes among such codes with respect to the Hamming and $b$-symbol distances.