Dimension of the Hermitian hull of constacyclic codes with length $n=\frac{q^4+1}{2}$

Abstract

In this paper, we present a new classification method for the defining sets of η-constacyclic codes of length $n=\frac{q^4+1}{2}$. This classification can simplify the calculation of the dimensions of the Hermitian hulls for these codes, while deriving the numbers of sharing pre-shared maximally entangled states of the corresponding entanglement-assisted quantum error-correcting codes under various design distances.